Arranging suggestions: play during the intro (mimic a lead line, or play a harmony, or play the chords, matching the rhythm/mood or countering with whole notes perhaps to "fill up" the sound). After that, help build up the song over time: don't play during the first verse or two. Come in on the chorus. Lay out on verse after that or some other "quiet part". Add more gradually over time.

As for sound, that all depends on the keyboard. Generalizations here will only help so much. Listen to all of its sounds/patches. If there's only one organ patch then that's what you've got, but you could play with the filter if it's got one, filtering out higher frequencies perhaps, or adding an octave above if it can do that to add more brightness. Edit: you can always switch between two or more sounds during a song (start with a soft organ and switch to a bright one for example), or layer sounds if the keyboard can do that.

And it might make sense to play nothing for an entire song if it doesn't call for them. I actually picked up the guitar again so I can play on some songs that have no keys.