Probably an amalgamation of everything I enjoy (which should also answer the next part), if I can. What I play alone is pretty much just sheet music I can find for what I hear, so influence is pretty direct. In a group, I might be more willing to bend to something like punk rock or some of the less tripe pop. Depending on the size of this group, some classical would be lovely!
I think I’d take the Gorillaz approach of having a core group, and then shifting in and out all sorts of talented musicians to play all kinds of music. Stand out from the crowd by becoming all the greatest parts of said crowd.