RTA Guide/Virtual Console
The Virtual Console is the second official re-release of Super Mario 64. It is the overall fastest platform for speedrunning Super Mario 64, due to its lack of lag and fast loading times.
Consoles
Super Mario 64 is available on the Virtual Console service on the Wii and the Wii U.
The Wii Virtual Console is generally preferred over the Wii U because of the Wii U's inherent 4–5 frames of input lag caused by syncing the game to the Wii U Gamepad. GameCube controller support on the Wii is also a major advantage because despite the Wii U having an official GameCube controller adapter, it is not compatible with the Virtual Console service.
Setup (Wii)
Software
Hardware
You will need a Wii that has GameCube ports. A GameCube controller is required for a basic setup, but by default, the analog stick mapping on Wii Virtual Console is inaccurate to the original (N64) in a way that makes tilting (for e.g. speed-kicks and quick-turns) harder. This is rectified by using an ESS adapter, which remaps this to be more accurate to the original. The generally recommended one is manufactured by Electromodder.
An ESS adapter not only allows (1) stick mapping correction, but also (2) the use of an N64 controller (as well as GameCube controller), and (3) input display.
Game Versions (Wii)
There are 2 versions of Super Mario 64 that were released on Wii Virtual Console.
NTSC-U
This is the North American release.
NTSC-J Shindou Edition
This is the updated Japanese release that includes support for the Rumble Pak. This version has removed the ability to perform BLJs, so 0 star, 1 star and 16 star cannot be completed. It also longer loading times than NTSC-U and NTSC-J, and slightly less lag in some sections. This version is only faster in some single star records, but in a full game run it's best to be avoided.
The only version that Virtual Console speedrunners should be using is NTSC-U. It is faster for every category.