What one thing would you tell someone like me before they sit down to read the Player's handbook?
As someone who greatly enjoys 4e, I'll echo Piratecat and say, "Don't read the whole thing." Unless, that is, you love reading what amount to spell lists. Reading the entire PHB seems like a very unpleasant way to spend your time.
The class descriptions will give you a good idea of how a class operates. I wouldn't read past the first 3 levels of powers for any classes you're interested in.
Examples: What one expectation should I set aside?
Saving throws are different. Conditions (apart from Slowed, most of the time) are, arguably, more important than damage for most classes. Also, small bonuses to-hit are
huge. Large bonuses to hit are probably the best benefit in the game. Because combats last longer, a slight shift in percentages can make a huge difference.
What's one cool thing to look out for?
Interactions, IMHO. Try to figure out how a group of characters can work together as a team. As a very simple example, a Warlord's Wolfpack Tactics mean that their Rogue buddy will almost always be able to sneak attack.
What's the AoO or THACO of this edition?
I've been playing for long enough I don't remember... Sorry. :/
What character class should I play and why?
It depends on what you want to do. I'd look at one of four character classes (just personal preference)
Fighter: I think every group needs one. Seriously. Fighters are a lot more tactical than most other classes, and though you may get some damage envy, I don't think you'll be disappointed. Fighters control the whole battle. (As a note, use a shield. You'll be attacked a LOT.)
Rogue: Again, you have a lot of tactical options. You can do an astonishing amount of damage with a Sneak Attack, and you have a few options which make this potentially one of the most entertaining classes in the game. Both "builds" work - just be sure to pick up the attack vs. Reflex.
Warlord or Cleric: If you want to get into the middle of fights and boss people around, take Warlord. Tactical warlords are best if you have someone else who can do healing. Inspiring warlords are probably better if you don't. If you want to really dominate with healing and crush undead, Clerics are pretty amazing. If you go Cleric, concentrate either on your Wisdom-based attacks or on your Strength-based attacks. Don't try to do both.
Wizard: Yes, they get criticized a lot. They are not always the most powerful characters, but then again I don't think they're always played right. If you try to build a wizard like a striker - that is, concentrating on damage rather than on special effects - you will hate it. If you concentrate on effects, you will probably love it. Orb wizards are my favorite. Staff wizards are also excellent. Wand wizards, I'm less impressed with.
If you want interesting stuff to do, stay away from Rangers. If you want a very simple character, on the other hand, you can't lose with them. Arguably, they're the least-tactically-interesting class in the game - particularly the Archer ranger. They set up interesting tactics for everyone
else, but you might get bored just rolling attacks and damage.
Paladins have some flaws, but if you are short-handed, they can do a decent job as a hybrid fighter-cleric.
Warlocks can be amazing, but IMHO they're kind of a fifth character, once you have all the other roles filled. Still, they're my favorites - they have more flavor than any other class in the game.
I hope this helps!
-O