So, mod mechanics. Let me just preface this by saying, due to the mechanics of the game, if you spend enough time on anything, it will eventually become a beast. So mods remain relevant through the entire game.
Mods will, in general, boost things by a percentage. Due to this, base stats are king. Keep this in mind.
First thing you need to know for weapon mods. If you find any of the mods Serration, Hornet Strike, Point Blank, Killing blow or Pressure point, never let them go. They boost base damage, apply before every other damage type, and as a result multiply later mods. Secondarily, mods called "multishot" mods are there. They add a chance for your gun to shoot more then one bullet at no cost to you. For shotguns, it increases the amount of pellets per shot by the percentage listed. So a 120% multishot mod would make any non shotgun weapon shoot an extra bullet all the time with a 20% chance of a third bullet. For shotguns it'll increase the amount of pellets by 120%. Multishot mods are amazing for shotguns, and almost equally amazing for every other weapon. They are the primary reason that guns can outdo melee so heavily. Pretty much any multishot mod is a godsend and they should be getting onto your weapon, after base damage mods, ASAP. Expect to work for them. After this, bane/expel/cleanse/smite apply right after the previous mods (known as base damage mods, these mods are tpically known as "banes"), and as a result are also of a decent priority. After THAT, elemental damage mods apply. Some of the new corrupted mods boost, I believe, base damage even more, but it's possible they apply after base damage but before banes. These are just educated guesses.
Despite all this above chatter, elemental damage mods are not useless! Far from it. Armor Piercing (for all intents and purposes an element) should always be on any weapon that doesn't armor ignore, and even on some that do (Namely, anything that does physics impact damage. A select few grineer units will still apply armor to that damage type.). After that, cold damage tends to be preferred for burning through shields, and primarily, the slow. From there it's up to you. Elec will stun corpus reliably as long as their shields aren't up, fire will stun grineer sort've reliably and apply a very weak DoT (I think). The DoT is honestly not worth considering, if it exists at all.
On to crit mods. Crit chance increasers are a multiplier. Not a direct increase. So a fully leveled crit mod will not give you 100% crit chance. It will double your current crit chance. As a result, crit weapons tend to have 15-20% crit chance at base. More if you're getting into broken stuff like Soma and Strun Wraith. Crit chance is a definite factor in weapons. Crit damage works like anything else, and I believe is applied at the tail end of the damage modifications, with elemental damage, so it doesn't multiply anything, it stands alone. Note weapons also have a base crit damage multiplier! Some weapons are definitely made to be crit machines.
Honestly, stacking damage is about all you need to do with most weapons. For less standard weapons, like say, grakata, you might need to put an ammo booster and a recoil reducer on it to get it to a good place. Just look at what your weapon does, and compensate for what you don't like! For instance, the lex has rediculous recoil. I personally don't mind it, but if you do, pistol stabalizer! Boom! Sure, it doesn't do as much damage as it could, but you enjoy using it more, and that's the point.
You don't have to use the super mega kill everything weapons except, maybe, in high end missions, and even then, if you don't want to, the only problem is that your weapon doesn't have enough forma on it. (You can get forma for free from orokin void missions in the form of blueprints, and log in rewards.)
So yeah! That covers Weapon mods. Warframe mods... well I can go over them quick.
Again, base stats are key. Don't use an armor mod if your warframe has 10 base armor, don't use a shield increasing mod if your warframe has base 100 shields (well okay, maybe you should, but this is like the only mod it applies to) etc.
The exceptions to this are ability power increasing mods. There is an ability power mod for everyone. Don't use your abilities for offense? Get an effeciency mod! Use them for offense? Get a power mod! Use abilities? Get an energy increase mod! This is what the majority of your warframe slots will be used for, just because most warframes use abilities, and the abilities tend to be their most powerful parts.
You could make a case for particular builds for stuff like berserker (melee builds love it), fury (more energy is always great, taking health damage not so much. Pair with a vitality mod and an armor mod for a maybe decent not cookie cutter build!), equilibrium, so on, but by and large you want ability boosters if you want something nice and easy to use. There are alt builds, but even those will tend to slot SOME ability boosters. Another small hint, you don't have to slot ALL your abilties. Most frames don't, in fact! Excalibur's will rarely slot super jump, Mag's don't tend to slot bullet attractor OR shield polarize (they're both good skills, mags have just become enormous damage cannons lately, so they'd rather put those points to more killing) etc. Don't be afraid to remove skills you never use! Just be sure to try them out before you decide they're useless.
So that's that. Another guide sometime in the future maybe. Going over specific frames? I could do that. We'll see.