My hunch is it'll be tough to find an internship in the flight ops department of an airline. Most of those seem to go to flight students at UND, ERAU, Purdue, etc. Don't let that discourage you tho.. while an internship would be a good way to meet some people, it's certainly not a requirement.
Your senior year would be a good time to look around at dispatch schools. You'll have to turn 23 before you can get (or at least use) your license. If that gives you some time after you graduate, I would strongly recommend doing what you can to make your financial load as light as possible. Also think about working in crew scheduling until you turn 23. That'll get you in the SOC with Dispatch where you can gain some exposure.
After dispatch school, there are several routes you can go, which were touched upon in previous replies. There's one other thing to take into consideration.. some airlines only hire dispatchers from the inside. So if you have your heart set on Delta or Southwest, consider an entry-level job at that airline.. or, even better, consider going to a regional to gain experience, then moving to that entry-level job.
As for choosing your first carrier (if you have a choice!).. I might be flame-broiled by folks at the smaller carriers for saying this, but.. I believe one of the "mega-regionals" will be your best bet. Airlines like Continental Express, ASA, Comair, SkyWest, or Eagle. Those carriers will provide you with a combination of experiences that you just can't get elsewhere.. like dealing with LGA
, international flights, 27-minute and 2 1/2-hour legs on the same desk, and watching your 6 ORD
inbounds all spinning at the same time.
Lastly, I know this counts at pretty much any job, but I've seen it magnified in our small group.. a good attitude and enthusiasm are *very* important. You'll like the work a lot more if you're earnestly interested in it. You'll also do a much better job, and.. you'll be a lot more fun to work with! heheh