Thanks for the info guys!
The HD 1.5 ReMix collection for PS3 is a good place to start, then the HD 2.5 set. Both sets have 2 full games and one cutscene compilation "movie" each. Then all you would need is Dream Drop Distance for the 3DS. However if you wanted to actually play 358/2 Days and Re Coded, they are both available for DS (and should be pretty cheap by this point).
Here's the order I would recommend playing them in.
Kingdom Hearts 1, Chain of Memories, Kingdom Hearts 2 or 358/2 Days (Days is actually a prequel to 2, but it was released after so it contains a number of spoilers that weakens the impact of some story elements in KH2), Birth By Sleep, Re Coded, and finally Dream Drop Distance.
Getting a bit
'ed here. I've gotta be faster! (I can get pretty long-winded about Kingdom Hearts, lol)