>Red Rescue TeamGBA version of the first PMD. Only uses one screen and has different renditions of the music which are either worse due to the GBA's mediocre audio or better due to instrument choice.
>Blue Rescue TeamDS version of the first PMD. Has a top screen used for tools like maps or team stats. Better audio overall.
>Explorers of Darkness/TimeOriginal version of the second PMD everyone forgot about. Has nothing Sky doesn't have apart from Meowth and Munchlax being available as the player character.(Sky still has them as partners)
>Explorers of SkyRemake version of the second PMD. Best game so far. Adds a lot of extra features, dungeons and Special Episodes which focus on secondary characters in the game.
>Gates to InfinityThird PMD game, reception is mixed. Removed some features and has a small amount of available Pokémon due to the switch to 3D. Plot is still good but text scrolling is atrocious.
As for order to play them in, pretty much what
>>23545672 said.