-how's the learning curve? will it take a while to get good enough to play online?
Learning curve isn't that difficult. Pro servers and lobbies are for veteran players, but you won't usually find those just picking random servers from either the list or the "Join A Game" button. It's not likely you'll be top of the leaderboards any time soon, but you probably won't be terrible. It's easy to start playing and become a good player, somewhat difficult to become a master.
-what classes are best for a newbie, and which are most useful long-term?
Soldier, Demoman, and Heavy are probably the easiest to play, but Medic's the best to start out with. You learn the role of Medic and how important he is to the team and free up other more experienced players to be killing roles. They protect you, you run around making sure everyone's healed up. You learn about pushes, teamwork, how enemy players attack and how best to dodge them, and you can take more time observing all of this running around making sure your healing stream is on the heavy or some such instead of running around trying to hit scouts and turrets and snipers with your guns. You'll spend more time alive than waiting to respawn (unless they've got some excellent spies/scouts). You'll also learn that communication is a big role in keeping your team alive.
Most useful long-term is whoever you find yourself playing best as or most fun with. I've changed my favorite guy so many times over the past two years. Started with Medic then went to Pyro then became a dedicated Demo long after the WAR! Update, then to Engineer, then Soldier, then to Pyro again, now I'm mostly a Pyro/Spy with some Heavy/Medic/Soldier play (I've totally forgotten how to play Demoman even though I have over 125 hours with him)
-any general tips I should know?
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“So we’ve cornered Andy and Kyle in the Swarts stairwell and then this guy comes out of NO WHERE like ****ing Batman or something.” ; ExTha is the man