I worked on a similar project
http://tonightsplaylist.com during a Seattle Startup Weekend(hopefully okay to link). Eventually people lost interest and we never fully developed the idea. My guess is the same will happen to your site with time.
There's so much legal BS you have to go through with any site like this, that legally you probably can't play any of the full songs you are currently playing (we scraped ours through youtube). If you use grooveshark you're probably breaking the law.
You could make some money by displaying only the samples of songs with links to buy the full song through amazon.com or itunes.com like pandora does but no one wants to listen to short samples of songs they want the whole thing.
Our plan for monetization was to get commission on concert tickets by pulling people's IP address and letting people know when their favorite bands they like come to town. Ticketmaster eliminated their affiliate program a couple years ago. There was another site that paid a commision on concert tickets we found but didn't implement(coudn't find it in my email after 5 mins of searching I'm sure someone else can post). Songkick.com's API may be helpful if you go this route, but they have restrictions.
My guess is the best way to make money is actually just pandora style charging subscribers or display or sound ads but you'll never get enough users to make it worthwhile. Good luck.