If you're familiar with any Zelda game I wouldn't worry about playing oot first. (But I would still suggest playing it if you enjoy retro games) They tell different stories and happen in different worlds. Majora's mask does build on mechanics you would have learned in oot but it's not essential. They do make the occasional reference to oot. (To save dev time they recycled a lot of the assets from oot)

I'm glad you had fun with Luigi's mansion. I never got too far playing as a kid. But I had fun playing the new one with a buddy.

In my opinion, the GameCube version of Majora's mask was the best one. It's still a N64 game under the hood but the controls feel nicer and the game runs better.

Edit: some emulators don't handle the clock correctly in MM. If you feel like you're always running out of time or rushing. It may be a bug!

Also there is a PC port of both oot and mm. But I've not tried it