http://www.gog.com/forum/myst_series/realmyst_vs_myst_masterpiece_edition/post2 The original Myst only let you navigate stationary screens, with you clicking on stuff and zapping around.
Myst: Masterpiece Edition remastered this game, with 24-bit color graphics, 16-bit sound, new sound effects, and a built-in hint system.
http://cho.cyan.com/RAWA/MystCompare.html RealMyst made it so that the entire world was now 3D rather than stationary, you move the mouse to look around and use WSAD to move.
http://i.stack.imgur.com/oRTWd.jpg RealMyst: Masterpiece Edition the best one, in my opinion. It both has the world remastered and in 3D.
https://i.ytimg.com/vi/W79CC2EW4vo/maxresdefault.jpg Also, the RealMyst games include an extra age, Rime, which when beaten, gives you a small glimpse of the next game, Riven.
Honestly, I see no real reason to play the original or the Masterpiece edition outside of nostalgia or wanting to play it like it was when it first came out. You could get RealMyst, but in that case, I say the best way to go is RealMyst: Masterpiece Edition so you get the extra stuff as well.