Nintendo 64 emulation has always been rather spotty and complicated even on PCs, and only recently bigger strides were done in favour of accuracy. As such, I don't think there's a definitive answer.
Wii VC for N64, as far as I know, is pretty great. Wii U VC is a little worse - official games have this weird dark filter and there's a big more lag. For most games it feels negligible, but specific ones may feel hard to play. I tried playing PAL Paper Mario and couldn't fit the life of me hit some action commands, something that never happened to me on original NTSC hardware.
There's an injector for Wii U VC for custom ROMs, but any game that wasn't released natively on the system may present minimal errors. Smash Bros works fine, but the ending image is tiny. Ogre Battle 64 works perfect since it was officially released on that. Perfect Dark is downright unplayable.
There's also a homebrew N64 emulator for Wii (I think it's called WiiSX64 or something like that?) but I never tried it so I can't vouch for its quality. I do know it supports some different stuff like 16:9 and such.
I think try the different options and see what suits you best. I'm personally satisfied with the Wii U VC for most of my N64 needs, and the games that don't work on that I try to emulate on PC instead.
Everything else Retroarch is your best option. Might also add PS1 support might be dropping soon (take a look at the Retroarch thread for more info) and there's also a PPSSPP port for PSP, but that only got one release so only a few games work perfectly.
I really feel compelled to respond to this post because it's info is pretty outdated. To start, Wii U VC is actually better than Wii VC. Yes, by default the Wii U N64 VC titles have a dark filter over them, however you can remove the dark filter and optionally make any N64 VC title be widescreen, see here:
https://gbatemp.net/threads/wiiu-vi...re-dark-filter-and-widescreen-support.517158/ So if one is to go the VC route, I highly recommend going with the Wii U titles as they'll be playable with your gamepad and Wii U pro controllers, have more compatibility (titles like DK64 being available for example) and look and play pretty much perfectly (granted some extra easy work is required to remove the dark filter, or you can easily find them already removed on a certain iso site.
Can't really speak for your PAL copy of Paper Mario on your Wii U, but I can confirm that my Wii U VC NTSC copy of Paper Mario on my NTSC Wii U does not yield any such delays.
Finally, the emulator you speak of has been labeled Wii64 in the past with multiple forks popping up since its inception, including Not64, Wii64 Rice, and Wii64 Glide. If playing on the Wii U, make sure to launch the overclock homebrew app before launching your N64 emulator for better speeds then you'd see on the OG Wii using the same emulators. If installed as a Wii U channel and using the later builds, you can indeed use your Gamepad or Wii U pro controllers on these emulators built for Wii hardware as well. I've found Rice to be the best version, but I haven't checked the others very recently so they may have gotten better. But I will say, that the Rice version allows you to play Goldeneye beautifully, something that neither Virtual Console will ever allow at this point. As such, I'm a person that makes use of both Wii U virtual console and an N64 emulator.
To your last point, I don't entirely agree. Retroarch is nice, but it's a bit too much in terms of all the options it offers, many of which you'll never use, making it a messier emulator than it needs to be. As such I recommend for individual systems, like NES, SNES, Genesis, and GBA for people to download the Wii U launchers of the emulators of these systems built for the Wii (FceuGX, SNES9XGX, Genplus GX, and VBAGX), when you install these as Wii U channels, they can maintain Gamepad and Wii U pro controller compatibility, and these emulators are all essentially full speed perfect emulation across the board, I'm sure there is a hiccup in there somewhere, but overall they're perfect, and they have so much nicer GUIs. (Plus I really like each system having its own channel on the Wii U menu, but that is definitely a personal preference).
Finally, there exists a Playstation One emulator already that functions like the Wii64 emulator, titled WiiSX, with the latest better fork being labeled WiiSXr. Compatibility isn't the best, but there are a decent amount of games that run full speed, and again, when installed correctly can even be played with your Gamepad and Wii U pro controllers and be overclocked for better speeds on a Wii U. All this info can be tracked down at that certain ISO site.
