My best advice to you is to play medic. Why, you ask?
If you've never played FPS style games before, getting a handle on the controls matters, and you should do that first with whatever you need to. However, once you know where you're looking, how you move, and how to fire your weapons, you need to play medic.
Someone early on in this thread said that the best way to learn is to study the best players of a certain class, and that's absolutely correct. However, not all classes have a 'best' player. I would say some do, but there are others that have a few different players who are at the top of their game, and these players may have different styles or preferences. That's the great thing about TF2; there's no best way to do anything. it's all about interpretation, and while some people have certain methods, not everyone is going to agree with them. So, learn from those 'best players', certainly, but take it as advice, not absolute rules.
Now, back to why you need to play a medic. What better way to observe the pros than to pocket medic them? I learned a LOT about how to play a heavy properly on Blackmesa by playing medic with some excellent heavies, and now, I consider myself a decent mesa heavy, where with a good medic (and even sometimes without) I can get a KDR in an evening of 5-6, which I think is fairly solid. Playing a medic is a great way to learn to play (through observation) soldier, heavy, pyro, and demo.
As for the other classes, it's all about getting out there and doing it. you can read all the guides as much as you like, but experience is definitely the best teacher. The caveat here is Engineer: I would advise that to learn the best way to play engie, you play with OTHER ENGIEs. As long as they aren't selfish (which some sadly are) it can give you a very positive experience, and you can learn the class well. Also, playing with other engineers will give you an idea of what makes for a good gun placement and what doesn't.
My last piece of advice: Play blackmesa with some caution. It's a phenomenal map, but it's very complicated. My advice would be to download it and play it by yourself for 10 minutes or so, just to get a feel for the level. However, once you know your basic way around, it's probably the best place to learn on eGO servers. The best players play there, which means the best people to learn from play there.
http://stats.edgegamers.org/hlstats.php?mode=mapinfo&map=cp_blackmesa_final&game=tf
http://stats.edgegamers.org/hlstats.php?mode=players&game=tf
the first link is most kills on mesa in the past week, and the second link is top 50 players on our servers. If you look closely, you'll see that there's a ton of overlap.
, good point 
