Well...there's relatively little I know how to play, so I'm frequently a bit at the mercy of the instrumentalists I'm singing with.

But, given my own preferences...

I'll play and sing anything I like. I know people who refuse to play anything that isn't sufficiently obscure--this always strikes me as rather pretentious and silly. Why refuse to play something just because other people like it? Rather ridiculous, I think.

As for requests--I'll play or sing them if it's a song I know and like. Otherwise, it's just a nice smile and "Sorry, I don't know that one well enough to do."