Ooh, toughie. Gonna say 3rd gen. though, because I love all three (until Torchic evolves), while I only really like Turtwig and evos. (though Infernape is awesome~).
Battling competitively or competitive battling?
If you ask me, battling competitively = just as it says, except one may not necessarily pay attention to all the stuff competitive battling does. So someone who battles competitively might have a team with sucky IVs/EVs/natures/etc. but they still enter tournaments and all that stuff to win nonetheless. And despite what competitive battling implies I think you can still have fun doing it :3