Yea you can jump into ds2 directly (altho i still think original ds is the better game).
Kh is a bit tricky. The story can be confusing if you didnt play the ps2 games. Instead, i really suggest playing the just-released ps4 game, KH1.5+2.5. It contains all the story til the next kh game (2.8 & 3)
Just look at metacritic highest rated ps3 games list. Aside from cod and ac series, i recommend trying every single game that has 90+ rating