In Classic, playing different classes actually feels different in more ways than just their abilities, at least if you think about it a little. Playing a priest, you really want to find a group because that's what the class was designed for, which is both good and bad - you're stuck very slowly leveling if you're solo, emphasizing the frustration of the slow pulling, but having different classes require different gameplay can be good. If you want to play a priest you're going to have to be more social by default, just whisper the guy you see killing stuff next to you and go level together, you'll immediately have a better time of it (this part is particularly exacerbated in the beta, as there are fewer players).
Only really to expand on GrĂ¡inne's comment as regards the 'collecting' and 'roster development' sections - which are, as said 'distinct' although they are intrinsically linked - I would like to point you in the direction of the in-game Achievements > Battle Pets > Collect tab. There are a series of achievements called Raiding With Leashes, pretty much all of which can be completed via the auction house - if you have the gold/inclination - or by completing old raids.