Welcome to Team Fortress 2! After nine years of development, hopefully it will be worth the wait.
Well, TF2 takes a horribly long time to download. It's annoying.
Something I found really helpful for when I started playing it is the TF2 Wiki, which has several useful strategy guides which are quite clear and not too long. They help point out simple things which you might have not found out until later.
I think a good class for starting up would be heavy or medic. Everybody loves medics. Although they aren't very useful unless you have heavies/pyros/demos on your team. Heavy is pretty nice to play, as aiming precisely isn't as important, and all of that health and fire-power can be really useful to your team even if you're pretty new.
I'd suggest waiting a good while before you try spy. In my experience, spies are the most difficult class to play at first. It will take quite some time to get the hang of it. But if you do then they can be great.
I'd also suggest focusing mainly on a single game-mode for a little while, as switching a lot can be quite confusing, especially since you don't know the maps, which at first may seem like a maze.
Capture the Flag is my personal favourite mode. I'd recommend playing that and starting on defense, as your base is generally much safer than anywhere else in the map. Plus understanding your own base in detail will better prepare you for understanding the layout of the enemy base, which is exactly the same.
Thanks and have fun!