In advance, my opinion is very biased for two reasons. One, i don't own a 3DS and will not buy one simply to play this game. Two, as one or two of you may know, i'm very involved in the collection, preservation, and of course playing of classic console games.
That being said, I think this remake will be pretty freakin cool, because Majora's Mask is one of my all time favorite games. Perhaps not as cool as the original though, because face it, it's the exact same game run through a filter...

http://www.nintendo.com/games/detail/l0_gKWzYFEFKk0MmdUSHMxOJkZg7Z-Rn
Ocarina of Time was released for the 3DS in 2011 (see link above). I believe in the recent video of the upcoming Zelda game for the Wii U, they said that they made some enhancements to the 3DS version of Majora's Mask (see WhiteboySlim's link below).
http://cheerfulghost.com/WhiteboySlim/posts/2320/new-footage-from-the-next-zelda-game
I never played either of these games on the N64. I actually didn't play them until they came bundled with other previous Zelda games as a pre-order bonus I got for Wind Waker (the GameCube version). I think both games are great, though. Sadly, my Wii U won't play GameCube games, so I'd have to hook up my Wii or GameCube to play them. I do own a 3DS, but the only Zelda game I have for it is Link Between Worlds. Also, i do not have the Wii U version of Wind Waker.
It would have been cool to see Wii U remakes of those N64 games, but I imagine they're so small that they'd have to find something else to fit on the Wii U disc. Perhaps that's why they released the games for the 3DS, but that's just my theory.
> what is your favorite Legend of Zelda game?
Hands down, Links Awakening. I play that every few years.
> Was this the game that Nintendo should have re-made?
Majoras Mask, for many, is a far superior game to Ocarina of Time. Since i've really only played Ocarina and a _BIT_ of Majoras Mask I am not such a gamer, that said Majoras Mask is a pretty popular game. So on one hand, does everyone that loves MM already own it and have played it a bunch? Sure. But the remake option does open up the game to a whole new audience and people that might not have access to Nintendo 64 hardware like we do.
> Should they have gone all the way and re-released it for the WII-U?
One good part of releasing it on the 3DS is the smaller screen size means it's a bit easier on the eyes whereas getting the image on a 1080p screen might not look as great. So, yeah, a possible re-release on the Wii U might be great and if I think I know Nintendo, they will.
As to why Nintendo chose this first? My thought it because, over time, Nintendo has re-released Ocarina of Time a bunch of times. So, maybe they were finally coming around to MM fans.