Shotguns are pretty cheap and an entry-level Rem or Mossy pump will do you well. I agree rifles are "better" in a lot of senses, but not an option in Illinois. Handgun hunting will be tough, and I think if you're going to the effort to learn to hunt you want to maximize any advantage you can. Best of luck whatever you chooose though.
I got into hunting at 21 with no guidance besides the Internet and mandated hunter safety - my hunter safety instructor basically said "just go for it" a week before my first turkey season when I asked him if I should bother. Didn't get anything (not surprising with a 5th season tag for my first time out), the birds talked to me a bit, and I learned a lot. So don't be discouraged if you can't find anyone to go with. Read the boards, grab a magazine or book or two, and have at.
If I could make a recommendation for Illinois: It's gonna be tough to find public land up north. Private land will be expensive, there's a lot of hunters with money to spend but nowhere to go so I imagine you've got some steep leases (I never even bothered to check). Kankakee's about as far up as I'd suggest hunting, although I imagine the pressure there will still be above average. I drove a ways, down to Pyramid State Park. I found two really good antler drops down there during my two turkey seasons - one six point with big mass, one five point with a busted brow tine but good length. Both would've been wall hangers if I had the other side. So I would happily hunt deer down there. And you can do it dirt cheap. PSP has a drive-in campground. I was in Champaign at the time so it was a hike, even worse from Northern Illinois, but I'd go down there for a few days, hunt the mornings, and try to get some work done and fish in the afternoons. I saw a lot more deer than turkey. There's a lot of open fields, a few good clearings, and some managed food plots. Lots of trails. Biggest state park in IL if I recall, never ran into another person except some horseback riders on a trail over a total of 15 days or so down there between scouting and hunting. Small town ten minutes from the campground with a gas station, a Burger King and a Subway - so if you stock your car up with water and breakfast bars what else do you need? Carbondale's a half hour if you feel the need to have a few beers and stare at short skirts after you tag your deer
If you really want to stay north, talk the forest preserve people in Cook County into letting you hunt that nature area off Ogden in Westchester/Western Springs. It's like a stinking petting zoo with all the deer, it's a horrible tease when I'm back in the area! Actually, though, if you want to learn to pick up deer sign and spot them a bit, it wouldn't be a bad place to check out if you're in the NE.
Anyway, good hunting!