Ideally, what would you be more keen to being exposed to, RedLemon? - original, parodied compositions, (which features witty lyrics) or actual game clips (which, at times, can be prone to featuring bleeps and bloops.)
True BGM and OST tracks from the official Mario Universe(s) are really nice starters and soothers (which can range from 8-bit
Gameboy white noise melodies, to mostly instrumental piano and orchestral pieces of the overworld/underworld/boss stages).
I also have a few videos/tunes that I have featured (and others which are still wasting away within my queue) in
The MK topic.
I'm not sure if I can recommend alternative websites/forums, but I first have to find it (a specific site that houses a huge library of video game music, which name escapes me at the moment).
Two 1-Ups to give you: I'd search for
Closer (to Mario) for a NIN-styled remix to the Library of Congress-preserved Reznor piece (obviously unofficial; also, it's not ground-breaking or anything, nor am I aware if the lyrics are clean, but for a 7-12 kid, I think it's an entertaining tune).
Last one for now:
This was apparently stuffed way down in my notes; I'm not sure if I have shared it yet. (yikes; it's quite impressive)