the easiest way ive seen to get new recruits is to just do the GS challenge log stuff. some are ridiculously easy.. so like.. do 5-10 punch gilgamesh games, enter battlehall and play like 5-10 triple triad matches (also nets good MGP btw).
After a certain point you don't actually ever need to get new recruits unless you're aiming for the unique outfit ones because you can change their class using the Contemporary Warfare logs (you get a couple from ranking squadron up, some can be rewards from deployment/chemistry, and once you're first lieutenant you can just buy them). Good diversity in classes is probably recommended. like you probably want 2 CNJ for when you do the high mental missions (or you can just not do those).
A good idea is to send all your squad members for the higher ranked missions at some point so they get new chemistry like conditional 50% DPS materia or whatever, and basically keep that chemistry so that you can use them to farm for items etc.