The games or the story itself?
For the games, there are a few versions of each game. For instance, the original Kingdom Hearts has it's vanilla version (just called Kingdom Hearts) and a "Final Mix" version, which is an updated re-release of the game including new features, bosses story and improved gameplay and graphics. Then there is the "HD 1.5 ReMIX" version, which is just a collection that includes the Final Mix version.
If you want to get into Kingdom Hearts then I recommend you get a PS4 as you can legit get the whole experience on that one console. Seriously, it's amazing.
You can get "Kingdom Hearts HD 1.5 + 2.5 ReMIX" which is a combo pack that includes those two previous ReMIX collections and thus contains:
-Kingdom Hearts Final Mix
-Kingdom Hearts Re:Chain of Memories
-Kingdom Hearts 358/2 Days (Not Playable, but does include all the cutscenes from that game in HD and a few more along with extra info)
-Kingdom Hearts II Final Mix
-Kingdom Hearts Birth by Sleep Final Mix
-Kingdom Hearts Re:coded (Same as 358/2 Days)
Then you can get Kingdom Hearts HD 2.8: Final Chapter Prologue, which is essentially like the ReMIX's and includes:
-Kingdom Hearts Dream Drop Distance HD
-Kingdom Hearts 0.2 Birth by Sleep -A fragmentary passage- (Completely new to this collection)
-Kingdom Hearts χ Back Cover (Original movie to explain the plot of Kingdom Hearts χ)