I'll try to explain most of this obligitory information.
With the advent of the Wii's certain death, coupled with the fact that dev. on KHIII won't even begin until the very end of this year, I can assure you there will not be a KH game for the Wii.
But Kingdom Hearts is one of those annoying franchises where you have to own a lot of consoles to be able to play the games, since there are a lot of main games on other consoles.
(There are not any remakes of the PS2 games yet, however rumors of HD remakes are thrown here and there because this year celebrates the series' 10th anniversary.)
(Chronological story order)
KH Birth By Sleep: you'll need an original PSP for this one. Not a Go or a Vita, since it's not even on PSN for purchase.
Kingdom Hearts 1: PS2 only
(I-suggest) Re:Chain of Memories: PS2
Kingdom Hearts 358/2 Days: Nintendo DS
Kingdom Hearts II: PS2 only
Kingdom Hearts Re:Coded (you can skip this one. Not important in the least): Nintendo DS
Kingdom Hearts 3D Dream Drop Distance comes out in the U.S. later this year for Nintendo 3DS :yes:
Hope this helped, and I'm not a crazy "know-it all" fan or anything
. This is all very basic information for a standard KH fan.