As far as I am aware, as long as you can hear the game audio, you're fine. Doesn't matter if you have other music or even background noise so long as the game audio is clear.

Non-stop 31 and 45 Star categories would be great!

Not sure what streaming software you use, but OBS has a built in noise cancellation filter that works really well.

The "Resources" section of this site (https://www.speedrun.com/sm64/resources) has everything you will need, especially since it has a comprehensive list of pretty much anything you'll need to get started and more.

Another great resource is Drogie's 16 star beginner tutorial video:

It's slightly outdated, but a great starting point. He also has useful links in the description of that video.

16 star is a great way to find out whether you really want to run this game or not, without sinking too much time in before you commit.

Is the ROM you are using NTSC? If it's PAL, it runs significantly slower.