The three main PRO's (Performance Rights Organization): ASCAP, BMI and SESAC all have licensing packages for unlicensed "college radio" stations. Check with your campus's student activities office first to make sure they don't already have a license from some or all of the PRO's. Then just call up the PRO's directly and ask; they'll usually be quite happy to help you give them money.
If you are webcasting...which you would be crazy not to; college students don't listen to AM (these days, they don't even own radios!) they listen on the web. Anyways, if you are webcasting, you'll also need ADDITIONAL licensing from the above PRO's and you'll also have to license with RIAA/SoundExchange, too.
You can find info about all this at
www.askcbi.org - CBI (College Broadcasters Inc) is hands-down the most proactive and knowledgeable group for webcast royalty licensing when it comes to colleges. I'd suggest signing up for their listserv, too. BTW, IBS looks like they are, but they've been known to take credit for CBI's work. FWIW, CBI is having their fall conference this weekend, so it might be a few days before the key people can answer any questions.
I don't know exactly how much this will all cost, but to make a wild-ass guess, it'll probably be $750 - $1500 per year by the time you add everything up. Maybe more, maybe less, but that's a starting point.
Call letters are indeed only issued by the FCC to licensed radio stations. Unlicensed stations may use any call letters if they wish, and some have done so for over 50 years. But they have no legal claim to them, and a licensed station can elect to use them at any time. There may also be copyright issues there, too - I would suggest that if you plan on using call letters to make sure that NOBODY else is using them (
search here) and make sure you can get the related domain names (.com, .net, .org and .fm) first. That way you should have sufficient legal claim to "we were here first" in any copyright disputes.