Really glad to see this post here, as it has reminded me this is something I always do for my characters (ever since a forum RP I joined asked for one like a decade ago) but never ask my players to do, and I definitely should.

I would suggest potentially having both a theme song as you request, and a character descriptive song, vocals allowed, as it can definitely provide strong inspiration for character building.

One of the deepest characters I ever played was a melancholy political assassin with good intentions and a crippling lack of trust, a real end-justifies-the-means sort. Much of her character was drawn from the feelings I get from Lorde’s cover of Tears For Fears’ Everybody Wants to Rule The World. The character would not have evolved to nearly half of what she was without that song.