If you listen to the recording(s) of the song that you like you can focus on the background accompaniment and hear what's going on there. Get some inspiration from that. Also, listen to lots of other songs with accompaniment and notice how the instrumentalists are in the service of the singer, not promoting their own axe! It doesn't matter what instruments are used. Accompanying songs, I find, is a damn sight harder than just playing tunes. There's many a potential pitfall that will have people talking about your bad taste behind their hands... Been there, done it, got the t-shirt!

Clichés are good here too. "Less is more" is a good one to start with! ;-)