im not realy one to ask about the distortion, but I think radiohead use turbo RATs.

for distortion I use a RAT II and my band play just general alternative rock, we do weezer, pixies and smashing pumpkins covers, and the RAT II does the job for me.

I think for muse youd want something more fuzzy, but id still recommend a RAT II as its cheap and versatile, you could get muse sounds on the very high settings

Im sure some more knowledgable people will post soon