Buying an iPhone off Craigslist?

Well I currently have the Galaxy S3. And I have had it maybe a little less than a year, maybe more. I'm with At&t and it's a 2-year contract before replacing and trading in for a new phone, and I have been having way to many issues with the one I have. I have backed it up, restored, etc. And I have my graduation party coming up shortly, and I was looking into just purchasing the iPhone itself. Though I know they are very pricey in general but a lot more just for the phone at the store. I'm still on my parents contract. I came across some deals in craigslist going a lot cheaper for the phone. Though the one I came across for the cheapest price is from Sprint.
When you purchase a phone, does it matter which company it's under or can you bring it to any phone company and get it set up? I know AT&T takes Sim-cards in there phones. But aren't all iPhones set up the same.

NO. You have to get it for att&t or else it won't work.