Ok, sure, sounds fun! I'll claim the first one while Khush is thinking about DK, and tomorrow someone else chimes in?
Day 1: Title Screen MusicSelection:
Metroid Prime (2002)
Linked here, and embedded below. Flows immediately into
this track.

This is a really tough one right off the bat. Obvious other Nintendo contenders would be
Ocarina of Time, which definitely benefits from an impressive video alongside it, and
Xenoblade Chronicles with its slowly building piano piece. I didn't pick Ocarina because, nostalgia aside, the quality isn't great with its tinny instrumentation (plus I think Zelda will get several other chances in this series).
Xenoblade, while great, I think also just works as a classical piece on its own, not necessarily as menu music specifically. (Plus, controversial maybe, but I like
Sorrow even better from that OST.)
Outside of the Nintendo bubble, I think the
Halo: Combat Evolved menu theme is absolutely iconic, although it's also the series' main theme for which I'll arbitrarily dock it a point. Also considered
Chrono Trigger, but again, it incorporates the main theme of that game.
Lastly, I don't know if anyone here ever played
Phantasy Star Online? I like this one for how very turn-of-the-millennium it sounds.
Metroid Prime, meanwhile, has a dedicated tune not just for its title screen, but also for the immediately following menu. Both tracks flow into each other really well, and perfectly set the atmosphere for this game. I consider them 2 parts of the same whole. Creepy, ominous, oppressive and distinctly catchy with a nervous, organic underpinning. Exactly how Metroid should sound.
Bonus link: if you're a music nerd, you should consider checking out
SynaMax on Youtube, who has found a lot of the synth patches used in Metroid Prime on machines like the Korg MS2000/MicroKorg, and software synths like old versions of Proteus.
The video I've linked includes some of the sounds used in the Title Screen music. Fittingly, one of the patches is called INVADERS.
Title Screen:
Menu Select: