Dragon Quarter is completely different from the others. Best I can describe it is like Vagrant Story and Parasite Eve. But the game forces you to restart at the beginning a lot -- it was done by the same people behind Dead Rising, kinda.
Dragon Quest is extremely retro, you played one you played them all.
Devil May Cry 3 is a prequel to 1, which is a prequel to 2. Just play 1, then 3. Avoid 2.
Kingdom Hearts is amazing, but make sure you play 1 before you touch 2, mostly for story purposes and the fact that 2 destroys 1. You could play Chain of Memories, which is like Kingdom Hearts 1.5, or you could just read a plot summary.