Tl;dr:

I heard the song "Frontier Psychiatrist" by The Avalanches and it immediately reminded me of your Bill- the artists make songs out of clips from old movies, and I feel like this one is a perfect mix of chaos, tragedy, Bill's childhood, and the Theraprism.

On that note, is there a specific genre of Earth music or an artist that Bill would listen to? We know there was music in Euclydia, but is there any flavor of human music he likes? (Or would at least tolerate?)

Boy are you ever in luck because I have a whole post about what (mostly human) musical genres I think Bill would canonically like. And an addendum. And what he'd think about dreamcore. And a few specific bands I was asked about. And the ONLY Lemon Demon song I'd ever add to his (and Mabel's) playlist. And I made a playlist of what I think he'd listen to, although it's really more of a small sampling of the kind of nonsense he'd play. And what songs he'd like playing on the piano, which is a different question from what he listens to. And a further addendum to the initial posts about his tastes, plus a mention of how, in fic, Bill's tastes would change due to being stuck with the humans. And a little summary of most of the above.

(And as long as this post is turning into a masterpost for my musical taste headcanons, I'm going to add my post about the Mystery Shack gang's musical preferences and Ford and Mabel's similar tastes and songs Ford would like but doesn't know about and a smattering of stray thoughts including about Gideon's tastes and Gideon's tastes part 2 and Gideon's tastes part 3 goddammit. And the next time I try to find all my GF music headcanon posts, I'll run into this post first and save myself time searching for the rest.)

tl;dr:

Based on the info we have from canon:

we know he thinks non-musical (to us) sounds make for some damn good music, but understands the difference between music he likes and objectively "good music" by human standards

he's into mid-20th-century music—but one of the first human songs he specifically highlighted as good was garage rock and he really hit his stride infiltrating the human music industry with motown, so I tilt him closer to the 60s than the 40s

he's into fun party music, which drowns out the screams in his soul

he doesn't say he hates country music, but he really gives off those vibes

He's heard listening to a fair amount of EDM despite claiming synth music is "painful," so I put the dividing line for "good electronica" and "painful electronica" around 1990 and have him steer away from new wave in particular

Addictive earworms are his enemy, and I like to imagine him battling them like how medieval scholars drew knights battling giant snails

He's fairly fluent in popular music in general and can casually drop song references into conversations with humans.

Outside the info we have from canon, I imagine he's pretty easy to get into new music as long as it's "fun"—he doesn't like broody downer sad songs—but I think getting him into 3 or 4 mad-at-the-world-and-your-parents early '00s alt-rock bands would fix him.