There's one sad fact, if we're going with 20 games like the SNES classic, a good half of those would be Rare games, and well, MS owns Rare.
That said, I would totally buy a N64 Classic just to salvage the analog sticks and jam them in my original N64 controllers.
I've thought about this question some since the NES Classic's release a while back as well. I think that if they make one drawing only from the titles they've re-released on the Wii and Wii U virtual consoles and such with presumably a couple of additions from Nintendo's release list, the N64 Classic will have a good but very incomplete selection of games. I love the N64 of course, and the games they have re-released include a lot of great classics! Again, looking at the current list of re-released titles, if they're going for a classic system with 15-20 games they could make a pretty solid one as is.
But yes, it would be impossible to avoid the elephant in the room, that an N64 Classic without Rare's games (except for DK64, since that is on Wii U VC) would be a critically flawed system, something missing many of the N64's most popular games. Coming to some kind of deal with Microsoft to allow Rare's other games on a N64 Classic probably would be nearly impossible though, considering how past discussions over the re-release of Goldeneye broke down for example, so I don't see a solution to that problem. Is there any realistic way to make an N64 Classic WITH Rare beyond DK64, considering the major hurdles that would be in the way?
Beyond that though, the other major flaw with the Wii / Wii U VC N64 library is that it is almost entirely first and second party. There are only two entirely third-party games that have been re-released on Wii or Wii U virtual console, Ogre Battle 64 and Harvest Moon 64. That's it. All other games on the service are either first-party titles or are games that Nintendo published in the US, and the rest of the third party library is ignored. I've always thought that this is a huge mistake, and that there are a lot of great third-party N64 games that deserve to be remembered and re-released! A couple of the more significant ones have been remade and re-released elsewhere, including both Banjo games and Perfect Dark on the Xbox 360, most of Rare's N64 games except for the DK ones on Xbox One in the Rare Anniversary collection, and Turok 1 and 2 on the PC and Xbox One, but there are many more deserving ones that remain unavailable. It's unfortunate that Nintendo has never cared one bit about that since starting up Virtual Console, and it hurts the service really. Some popular titles would have other issues, like how pretty much all sports games are probably unaffordably impossible thanks to licensing (which is a shame, for stuff like MIdway's great fun arcade sports ports!), but a lot surely could be rereleased if Nintendo wanted to put in the effort.
Here are the games Nintendo has re-released:
Wii and Wii U VC
--
Super Mario 64
Mario Kart 64
The Legend of Zelda: Ocarina of Time
Star Fox 64
F-Zero X
Paper Mario
Wave Race 64
Yoshi's Story
Sin and Punishment
Pokémon Snap
1080° Snowboarding
Kirby 64: The Crystal Shards
Mario Golf
The Legend of Zelda: Majora's Mask
Ogre Battle 64: Person of Lordly Caliber
Mario Tennis
Mario Party 2
Wii VC only (for whatever reason)
--
Bomberman Hero
Cruis'n USA
Pokémon Puzzle League
Super Smash Bros.
Wii U VC only
--
Donkey Kong 64
Excitebike 64
Harvest Moon 64
Bomberman 64
If we assume that Nintendo could use any of the titles on this list that'd make for a great library, but the criticisms -- for having no FPSes when that was one of the more popular genres on the platform, almost no Western games aside from maybe DK64, Excitebike 64, and Cruis'n USA when Western developers made many of the better N64 games, no Doom 64, no Turok (though with the remaster out now this would look dated in comparison), no San Francisco Rush, and of course no Rare... the criticisms would come fast and would be accurate. The N64 is my favorite console and I love a lot of the games Nintendo has re-released, but for maximum mass-market appeal they need more than this.
So what would I want... hmm... here's what I'm thinking at the moment, making a list but minus totally impossible stuff (licensed games, Rare, Wipeout) but with M-rated games (which Nintendo probably will avoid):
Super Mario 64, Mario Kart 64, Donkey Kong 64, Doom 64, Star Fox 64, Sin & Punishment, San Francisco Rush: Extreme Racing, San Francisco Rush 2049, Pokemon Puzzle League, Zelda: Ocarina of Time, Zelda: Majora's Mask, Goemon's Great Adventure, Excitebike 64, F-Zero X, Turok 3: Shadow of Oblivion, Bomberman 64, Paper Mario, Mario Tennis, Ogre Battle 64, Wave Race 64. There's 20. If you can have some licensed titles, then Star Wars Rogue Squadron (or better yet Battle for Naboo, which is less popular but a better game in my opinion) is a must-have; if you want to stick to 20, sub out something like the original SF Rush, or Bomberman 64, or something. Also they probably should include Mario Party 2, though I don't care too much for the series myself. Etc, etc, I could keep going.
If they want to do something really interesting, though: Custom Robo, translated! The two N64 Custom Robo games are fantastic, almost as great as the GC game is, and it's a real shame we didn't get them on the N64.
Or just come to an agreement with Microsoft and include Rare games.
Nintendo and Microsoft made an advertising campaign together about crossplay, which is something I never thought I would see, so hey, anything could happen. Still, in this case one of the XBox One's best selling games is Rare's collection, so its unlikely we would see anything on it on such a system, sadly.