For rocket jumping, just having basic proficiency with single jumps is enough for most people. It's just a timing thing with turning around, crouching/jumping, and firing that you'll get used to eventually. Work on gauging distance, height, and speed at first on various different maps to get onto ledges and the like. Rocket jumping makes the soldier the most mobile class in the game, much more so than the scout, but few people bother getting good at it to the point where that's true. You should really spend very little time walking places as soldier.
For more advanced jumps, two things are vitally important: relative projectile speed and air strafing.
Air strafing is simply strafing left or right while slowly and steadily moving the mouse in the same direction. It allows you to adjust your landing position and twist your arc mid jump. So, if you want to land to the left, you'd hold 'A' and move your mouse to the left slowly (or faster for a tighter spiral, but it has its limits). Never press or even tap 'W', as there are incredibly few times when that wouldn't be catastrophically bad for a jump. This is probably the hardest thing about air strafing for most people, is getting over the urge to KEEP HOLDIN DA W. If you ever want to use something like the market gardener, you'll without a doubt need to be a master of this, but it's also incredibly useful for getting a good position on someone to take advantage of their low health or vulnerability. Hell, you can use it as any class, recovering from being popped in the air or as scout during a double jump.
Most rocket jumps are chained; rarely is it best to just do a jump with one rocket. As such, you need to be able to gauge your speed against the speed of the rocket you fired. Often, you'll be moving faster than the rocket. This is one of the reasons why the direct hit and liberty launcher are rarely used by good soldiers, because rocket jumps are severely gimped by that projectile speed. Generally, the first rocket gets you off the ground, and the second one (or beyond) speeds you up and keeps the momentum going or changes height/direction. You need to fire the rocket ahead of you so that you get within its explosion at a good distance to get as much force out of it as possible. This is particularly difficult to master, more than air strafing.
For general soldier playing, most people abide by the simple rule "shoot feet get kills". If you can bounce somebody up, they're probably dead. The default rocket launcher is arguably the best weapon in the game, if you don't count the medigun/new quick fix (they're not really weapons anyway). If you're bad at soldier and don't want to get better, you can still have some fun with the liberty launcher, as it's by far the easiest to use. It trains horrible habits though, and almost anything that can be done with it can be done much better by a skilled player using the default rocket launcher. The most important thing to do is to get used to that projectile speed to land directs consistently.
I'd avoid heavy, personally. There a few times when heavy is a good choice. On particularly derpy pubs it can be stupidly effective, if nobody on the other team knows anything, but it's a limited class and any skills learned on it don't really apply to other classes. The only thing particularly skillful about heavy is positioning/timing and tracking, which pretty heavy-exclusive in a fast paced game with very few automatic weapons. Most people enjoy it at first as a class with a lot of health a gun that doesn't need much aim, but if you're TRULY COMMITTED (I had to laugh at myself there) to TF2, you'll get bored of it.
Pyro is another typical recommendation for new players that I don't agree with. The vast majority of pyros can be summed up in the phrase "W+M1". The flamethrower does so much damage with so little aim that really, most people just walk forward at people holding left click, and actually do pretty well with it. But, this teaches you literally nothing about how to be a good player. Quite the opposite. If you use the degreaser, the focus is on your secondary and melee weapons, which makes pyro a much more interesting and somewhat challenging class. You essentially become a fat scout with airblast and a killer melee. I enjoyed it for a while, but am pretty over it, but if I can make a recommendation, it's to use the degreaser. The rest are variants on the W+M1 concept that downplay airblast, which is quite important and enjoyable (except those dumb pyros that do nothing but airblast people for assists, they're as bad as pyrocars).
Medick. Only way to get good at it is to play it. Your main job is to keep your team overhealed, and to deploy timely ubers that spearhead a push. It's all about timing, and most importantly, positioning yourself to avoid getting killed. Dying as medic is the worst thing you can do. Medic is the most important class to have on a team, and a good duo can be godlike. There's an interesting kind of mating ritual that goes on with medics in pubs; they're desperate for good players to follow, and a considerate partner who knows how to treat a woman medic. Hats play a larger role in this than you'd think.
And uh, what else... sniper, if you want to get good at sniper, don't bother with junk like the sleeper, huntsman, or machina. These do sometimes have a role, but really, sniper is all about getting them headshoots. Generally, you want to know exactly where someone's head is going to be before you pull the trigger. Then it's simply a matter of timing (and ping/framerate).
Scout... aim and positioning. You need to get the drop on enemies, and score consistent 100 damage shots. I wouldn't play scout seriously on servers without random spread turned off, because who the hell knows where your shot will go off to with completely random scattershot. Probably my favorite class personally. Dies to a lot of random bullshit on servers with damage spread (125 damage nades ho!) and random crits, but few servers actually run no crits/damage spread/shot spread anymore.
Demoman... an easy class for moderately skilled players to dominate at, but truly good demos are distinctive. Demoknighting isn't really practical, but is great for the fun of it. Most people play sticky/nade demo incredibly spammily, which is irritatingly effective, but really, if they're good, it's not quite spam.
Spy... has many problems. Facestabs are so common that it's basically a random crit, and the entire nature of the class is centered more on things like luck and randomness than much skill. Since the disguise function is actually pretty useless against anyone experienced, it's all about using (imo) cheap tactics to get easy and safe kills. Or just spam the dead ringer. Over, and over, and over again.
Engineer... I don't like it very much. Kind of needed on some maps. Stupidly broken on others. Vital in most pubs. A decent engineer can delay a completely useless team from losing for quite a while, longer than if you played another class. Maybe even long enough for a turn around. Some people like it. Don't use the gunslinger, or I will personally slap you with a rotten salmon.
I actually haven't played in quite a while, but I doubt things are any different since the last real update.
TL;DR: Rocket jumping is useful, some other things are useful too I guess, have fun