The thing I've always wanted to bring to Spinning class was a new saddle. The wide-ass cushy things they have on most spin class bikes are truly awful. Unfortunately you probably won't be able to do that. As such: spend some time getting the saddle height + fore/aft adjusted as best you can.

Oh, also: if you are not familiar with riding a fixed-gear bike...resist the temptation to "coast"...though you usually learn this lesson pretty quickly