Yeah imo it seems to be just pick the one you like best. To me I like Pyro the best just because he seems to be the one who does the most killing and I find his gas expulsion thing pretty useful when I'm lighting people on fire and they start shooting at me. I also like Heavy only if there's a Medic on the other team that can back me up when I'm trying to hold up on a firefight involving like 5 people at once. The other classes feel unnatural to me though. Medic is pretty boring and I'll only use him if there's no other Medic on the team, Soldier's rockets don't do as much damage or don't go as fast as I hoped they would, I was never good with noobtubes so Demo is out of the question, I'm terrible with Scout because he's so twitchy and it's hard for me to get kills with him, Engineer only seems to be useful for making turrets and dispensers, which never come into use unless I'm playing something like CTF, I can't play with Spy because I can't sneak up for **** on others, and I can't use Sniper most of the time because I'm on enclosed maps and seeing as my connection isn't the best with this game, I can't be as precise with my shots as I want to be.
And imo, CoD counts as class based to a certain extent seeing as the slots for different weapons are called classes, and since there isn't as much variation on that than in this game