Yes you can choose, but you set it up on your PC, on Winamp for Windows or Mac, not on your phone. The setting on the phone is just there so that the Winamp program on your computer will detect and sync the phone.
And obviously, since I already said that its done via Winamp for PC, no it won't work with PowerAmp. But Poweramp can read the data synced via Winamp. For example, I have winamp installed but I don't use it for music. Its just there for wireless sync. I use Ubermusic for playing and it is able to use the playlists and music synced from winamp.