I'll try to sort the list of skills down from best to worst, since most of the time you just want to pick one or the other.
Also, here, I prioritize dodging over life for tanking... the reasoning being that a dodge will save you from a sniper headshot or bazooka, but not +10 life. Plus, it's possible to dodge every bullet from a minigun, whereas getting hit by several bullets will still kill.
I'll also prioritize initiative over speed. I think speed gives you a dodge bonus, but initiative lets you move first, reload first, and more importantly, shoot first. Speed is also not very helpful for guys who don't move, the aiming and reloading is based off initiative.
Mundane skills
===============
Skills available from level one.
Hydroshock shells: Probably THE best skill in the game, gives you a lot of instakills no matter what weapon you use. Maybe useless on bazookas, because bazookas are instakill anyway.
Tuck 'n' Roll: One of the best defensive skills, it's a complete lifesaver, and allows you to dodge miniguns, snipers, bazookas.
On point: +200 initiative is amazing, it'll ensure that they'll shoot, reload, and fire faster than most people could blink.
Rush: One of my favorite skills. Less so on a bazooka or sniper, as they don't have to move. It's one of the best skills to have on an assault rifle, because it allows troopers to run back to get over minimum range, but fires immediately while running away. It also combines extremely well with any speed bonuses, because it means you can run into range and get a free shot.
Gas grenade: The poison can often kill everyone in the back (snipers, bazookas!) allowing enough time for just one shot. Less useful later when there's doctors, but it'll still distract doctors for a few rounds and do hefty damage. Downside is that they don't trigger in every battle.
Twinoid: That poison hurts, but I've seen troopers fire off 3 shots from a single shotgun, including reloading!
Cold blooded: Yeah, double speed aiming is awesome on everything, especially the devastating and slow weapons like bazooka, sniper, and minigun.
Compensator: It's wonderful on auto weapons, mainly miniguns and assault rifles! 30% faster recovery is still excellent though, so it's worth it on slow weapons like bazookas and snipers, as long as you have the ammo for it.
Laser sights: VERY highly recommended for bazookas. Good on most weapons too. Not that useful on shotguns and sniper rifles, since they already have high aim.
Eye of the tiger: Similar, but weaker.
Loader: Instant reload... Extremely useful on machine guns. Good on one-shot guns too, like sniper/bazooka/shotgun, because it reloads fast enough to practically give you a second free shot. Just don't get it for the pump action shotgun.
Heat sensor: The 20% aim isn't so great, but the "can't be dodged" is! Even more so for a bazooka.
Adrenaline: Doesn't say whether it's speed or initiative or how high. But it sounds like it'd combo well with a dodger.
Scavenger: Disarm an enemy AND get a free backup weapon. Great early in the game against weaker guys, later on less useful when people (including your guy) has multiple weapons, and when saboteur disables weapons much more effectively.
Frag grenade: What it doesn't tell you is that the grenades always pop over people's heads and are often a headshot, actually doing 2-10 damage per frag. I've seen some nice headshot instakills from them, and even when they aren't instakills, they can finish off weakened targets. Would be higher if they hit more and triggered more often.
Flashbang: The blindness lasts long enough to effectively cripple an enemy long enough to kill them.
Take cover: Gives an amazing 50% dodge when they need it the most. At worst, it allows your shotgun guys to tank much better when reloading, which is what they're meant to do.
Frenetic: The 200 initiative is superb. Drawback is that you actually have to kill someone first. But it should go along very well with a sniper or rocket guy.
Sprinter: Speed isn't so great, but double speed is amazing to watch and will help in either running towards the enemy or running away.
Camouflage: 20% dodge, yeah. Maybe nice on a bazooka guy too, gives him time for that first shot.
Heartbreaker: The killshot bonus is great, just remember to tell this guy to aim at the heart.
Zigzag: Dodge bonuses are great, though this only applies when they're moving. Very good with shotgun guys, though.
Bulletproof vest: Reduced damage is nice. Doesn't protect against AP weapons, but who picks AP anyway. Would be rated higher if it didn't take an equipment slot.
Full metal balaclava: Ditto. But actually better, because headshots are more common AND it defends from the double damage to head.
Battle ready: Highly recommended on any weapon with more than one bullet... can't have enough on your first clip.
Nimble fingers: Worthless with single shot weapons. Excellent with weapons that have a lot of ammo to load like minigun and assault rifles, or some pistols.
Trigger happy: Great with some slow weapons like the snipers with more than 1 ammo or most of the pistols. OK on assault rifles too, not so useful on miniguns since their burst is high enough anyway. I'd rank it high on specialist sniper rifles, semi-auto shotgun, and assault rifles and pistols. Low on everything else.
Vicious: Good with most of the accurate weapons.
Sturdy: Highly recommended if you actually have a heavy weapon, not so, otherwise.
King of boules: Excellent if you have a good grenade. But some grenades have a large enough radius that they don't really miss anyway.
Toxic shells: Poison is a definite killer. Excellent on sniper, but I've seen it used surprisingly well on shotgun too.
Explosive shells: Double damage is incredible, but you're only able to double for 6 bullets. Still, it means an instant kill with all but the weakest weapons, great on low ammo, high accuracy weapons like pistol and sniper.
Smart: Ambivalent on this one. On one hand, it gives you an extra skill to choose from, keeping you from picking between two stupid choices. On the other hand, it actually uses up a choice slot. Later in the game, you get elite skills, so unless your > lvl 9 or something, it's usually worth taking.
Dodger: Only dodges one shot. Still... it's a guaranteed dodge, and that one shot is most likely either a rocket or sniper headshot.
Shock grenade: Nice area, and it'll disarm everyone long enough for your guys to either move in, or get a couple of shots ahead.
Heavyweight: Not fond of life, but 10 life is almost double. Speed penalty is a problem, but not so bad if you have longer range guys.
Bipod: Useful on all weapons. Might want to adjust your favorite target to try to hit fast movers if you get this.
Unshakeable: Since many hits kill, I don't think having lowered performance is your main worry.
Hard boiled: Ditto.
Grenade: Damage is poor, area is kinda too small, seen it miss too often to recommend.
Huge calves: Not bad, but there are better skills, and these don't turn the tide of battle.
Paralyzing shells: Paralysis makes them easier to hit, and keeps them from shooting back. But it seems to last much too short to be of any use, I see it more like a weak knockdown.
Glue grenade: Delay is nice, makes the enemy 'lose a turn', but lasts far too short to be recommended.
Tail gunner: Only works for automatic weapons. The 2 bullets will be less accurate, and use up more ammo..
Juggler: Switching weapons is fast enough without it.
Heavy armor: Speed penalty isn't nice. But the game doesn't seem to call this armor, so it may be immune to armor piercing. Maybe more useful on a sniper..
Survival Instinct: Speed is not so useful... and seeing how this only applies when you're injured, even less so, since the point is to run there before you get injured.
Lucky charm: It'll save you from early headshots, but then you'll still get killed over the tiniest fragment.
Brick shithouse: Hmm... 3 life isn't much, and they're often too spread out to cover each other.
Commando: 5 life stops only 1-2 bullets, and not the critical ones.
Motorcycle: Would be better if it triggered more often.
Thermos of coffee: Speed doesn't help much and this only wastes an equipment slot.
Enthusiastic: Again, speed.. and this one requires you to not be injured.
Bait: Making them easier to hit in exchange for life. Not a great exchange, even if that extra life lets you take an extra bullet.
Hats
=====
Available at level 6. Hard to prioritize because the choice depends on how they fight. Spy is horrible with snipers, doctors and munitions is bad with front liners, pilot is bad with a good character.
Scout: This allows you to bring in an extra guy! As long as you can afford more troopers, a scout is a great choice.
Saboteur: Disables weapons, pretty damn good choice. Plus, you don't have to keep him alive.
Spy: Excellent choice with a heavy damage guy, and that extra initiative really helps. Recommended with a shotgun or minigun guy with some initiative boosts.
Doctor: Good for mid-long range players who you don't expect to die early. I give my doctor a bazooka and assault rifle, lets him stay out of battle for one bazooka shot, then go in for the kills and healing afterwords. Oh, and doctors heal poison too.
Comms officer: Kinda weak, but a bonus is better than getting a worthless soldier.
Munitions: I'd get this just for the double grenades, especially if someone has gas grenades. Getting a bonus AFTER WINNING is a bit weak, IMO, but it could turn the tide late game. Plus, you actually have to keep the munitions guy alive to get that bonus.
Pilot: Putting a great trooper inside a tank is a bit of a waste of a trooper. No guarantee that you'll get a vehicle either. And when you do get one, no guarantee that they'll bring it to the battlefield. Still, every vehicle aside from a motorcycle is excellent, a drastic increase in possibly getting a tank is well worth it.
Soldier: 1 life is a pittance, 1 life per level even more so. Worst choice.
Elite skills
============
Skills that are available from lvl 5-7 onwards..
Voodoo doll: Double killshots on everyone!
Wife Beater: 30% speed is great, but the 30% dodge is higher than almost anything in the game.
Suspicious: Excellent late game skill, great anti-spy and anti-saboteur, and the immunity to friendly fire tops it.
Anatomy: Double killshots is always great, though it's not as good as hydroshock. But being able to hit your favorite part is excellent.
Martyr: 5 free guys with 150 initiative. Hell yeah. Too bad the guy actually has to die for you to get this, and you'll never actually have 5 guys in reserve.
Talky-Walky: Lets you have a free guy, great skill.
Out of Bounds: Ditto.
Crybaby: Ditto, but less useful.
Restless: 200 init is nothing to sniff at. Not sure how it works, but it sounds like it'd be great in large fights.
Helicopter: The vehicles really add a lot of firepower, though your trooper won't be using their other weapons while they're active. They don't activate all the time, though.
Fighter Jet: Ditto.
Light Tank: Ditto.
Heavy Tank: Ditto.
Rucksack: Never seen it in action, but giving everyone full munitions at the start of the game sounds great.
Covering fire: Anything that allows you more instant shots is great, never seen it actually in action, though.
Last Mohican: Not useful on single shot weapons, but on pistols and automatic weapons, I can see how this can be extremely devastating. Unfortunately, your semi-auto guys aren't expected to live to be the last person, unless they're a sniper with a pistol as backup weapon.
Grenade Benie: Really nice radius, damage is high enough to kill most troopers immediately. Definitely combos well if you have a munitions guy.
Clown grenade: That clown is actually quite tough and will keep many of your guys from dying.
Invincible: No instakills is especially nice on anyone. Won't help you with the rats, though. Or bazookas.
Interception: Considering how devastating grenades are, this is very much a lifesaver. But I haven't seen it in action, so can't recommend it yet.
Nervous: Emptying the clip can really kill, though most of the bullets will be rather inaccurate. Excellent in the right situations, though.
Black hole grenade: Well, grenades are killer anyway, so a confirmed kill isn't much of an upgrade. The zone is too small to recommend it over grenade benie.
Bounce back: Awesome, when you actually do get knocked down. Unfortunately, most knockdowns are already rather fatal
Hyperactive: Not sure what "interferes enemy" means. If it's throwing back grenades, bump this up a few notches. Still, 50% speed is decent.
Death grip: Never dropping weapons is nice, but that +1 fist damage is sort of like a free extra skill, so worth it just for that.
Vendetta: 50 init is moderate, and this assumes that your teammate is going to die first
Radio: Com bonus is nice, but it's dependent on luck.
Savior: Haven't seen this in action, so no idea if actually heals them to full health or just one point and such. If it's full health, I'd put this as a must have... though this also assumes that you're not the dead soldier.
Friendly fire: Considering how many friendly headshots with shotguns I've seen, there's a real use for it. If you have that blessed grenade, you should definitely pick this one up too.
Blind fury: You don't really get blinded that often, but helpful when you do get blinded.
Hurry: 10% speed is negligible. The double power use ranges from either very powerful or useless, depending on your trooper's skillset.
Healing Grenade: Not sure on the accuracy of this thing or how often it triggers, but healing can save a few troopers. And it relies on you keeping the owner alive.
Binoculars: One of the weaker skills to pull in other guys, especially with the init penalty, but still gets you an extra guy.
Armor Piercing Shells: Armor is too rare for this to be of much use. Maybe for a sniper attempting headshots..
Charge: I see it as a speed boost, but haven't actually seen it done to recommend it.
Amphetamine Boost: 500 turns seems a bit short. 100% speed is nice, but Sprinter is better for this if you can get it.
Trample: Not that good unless you have a guy skilled with knockdowns or maybe a scattergun.
First aid: By the time you use this, it's almost over.
Fall guy: Doubt you'd survive whatever destroys a vehicle anyway.
Survivor: Not so useful. Poison still kills them, and 1 life is only enough to be a decoy.
Commander: By now, you should have more battles than you need. Maybe more entertaining to watch..
Reverse attack: Don't see the point in this, except to support snipers and bazookas.
Occupation: 1 [T] is nearly worthless, now that you can win most battles, and do raids.