yeap, this should be the right thread to ask, although these informations aren't too hard to find online too.

1) The latest PS handheld is PS Vita, the successor of PSP( PSP have many version due to hardware revision ). PSV also has 2 version, 1k, and 2k. The main difference is 1k has better screen, 2k is lighter, and uses microUSB to charge
2) apart from PSP and PSV( old console and new console ), there are no difference among hardware revisions, like PSV 1k and PSV 2k are the same in gameplay
3) given recent discount, i think u can get new unit of Vita for 6xx.
4) Online feature is mostly for PS Vita, most the games these days allow you to go online and have coop mission with other players

note that all the new games will be out on PS Vita now, and PSP is already consider legacy console( correct me if i'm wrong ). I would definitely recommend PSV over PSP if you're buying it now.