I want to buy a Rayman game.
My own personal recommendations:
If you're feeling rather masochistic and enjoy Nintendo Hard games, the first Rayman will
destroy your hopes and dreams. I played the PS1 version myself, but the Atari Jaguar version was the original, and has various small changes.
If you're more a fan of 3D platforming, either Rayman 2 or Rayman 3 will do it for you. Rayman 3 has more focus on combat, almost like a beat um up, but has short puzzle like segments with the powerups. Rayman 2 is the go-to if you like it less linear, but not collectathon level, the combat is very simple but the narrative, world, story building, etc are an absolute joy. As a side note, there are various differences between versions of Rayman 2, the PS1 version has a lot of missing content, but also has levels unique to itself, full dialogue (in multiple languages, as opposed to gibberish), a completely unique second phase to the final boss, and a bonus scrapped 2D level from the original concept for the game (unlocked by getting 90% or so completion). The N64 version is the standard version, but if you want the absolute definitive Rayman 2 experience, the Dreamcast one is the way to go. There's also Rayman Revolution for the PS2, which is another unique entity, but brings aspects of each version into one.
Also, you'd do better to just get Rayman Legends (Wii U version comes highly recommended) as it contains almost the entirety of Origins, remastered (with the updated visuals and gameplay elements of Legends) so you won't miss out on much.
There are also the various handheld iterations of Rayman, all unique in their own rights. I believe a few of them are on the 3DS E-Shop (I know the original GameBoy Rayman is), but don't make the mistake of getting the watered down Rayman 1 port.
Rayman Arena is also a wonderful spinoff title with both racing and battles, multiplayer, of course. PS2/GameCube.
And if you, for whatever reason, have the particular urge to become suicidal, there's
the Rabbid games.
I hope this was of help, though tracking down these games is another story entirely..