EDIT: This PC Gamer guide was designed for the new F2Pers, and is pretty damn good about explaining pretty much everything: http://www.pcgamer.com/2011/06/24/the-noobs-guide-to-team-fortress-2-part-one/
For classes, I suggest you start with the Medic or Soldier. Medic is a decent way to learn the maps and gamemodes, but you’re going to be a target – never stop moving, and stick around strong attack classes (demo/soldier/heavy). Soldiers fairly easy to start with, not many quirks to the class – you have a rocket launcher, aim at their feet and beware of Pyros (they can airblast your rockets back at you).
I can’t remember if the in-game tutorials are much good, but they at least tell you what each of your weapons are and what they do.
As for drops – almost always, your defaults are the best. There are no straight upgrades (well, some can be argued); most weapon drops are designed to benefit you in one style or aspect of your game, but there’s always a trade off.