Which class should I choose?

Once you're in game, pick either team. You usually can't join the one with the most players. Then you'll have to pick a class.

A good starting choice is the Medic: you heal people on your team by firing a beam at them, and that's immediately useful and appreciated by your team mates. At the basic level, it's all you need to do. And that gives you time to watch how your team mates play, see who beats whom, and learn a bit about what the weapons do.

When you fancy a change, switch to Heavy. You're slow, and your gun takes a while to spin up, but once you start firing someone's usually dead by the time you stop. You're also the first person Medics will think to heal, and since you just played Medic yourself, you know how to be a good patient and keep them protected. It's a really satisfying relationship.

After that, it's mostly personal preference. Soldier's the best all-rounder, so another good early choice. Don't stick with any of them for too long until you've played all nine: each new one you try helps you understand the role of the others better too. Spy is probably the hardest to be effective with when you're a beginner, but he's worth playing just so you understand roughly how they work.

Some classes, particularly Spy and Demoman, work very differently once they unlock certain items. To describe all the differences would be long and pointless. But if a black Scottish cyclops charges at you with a giant sword, get out of the way. And if a you hear an electronic crackle shortly after a Spy appeared to die, he's alive, and he's behind you.