Will an unlocked Iphone work with t-mobile?

So here is the deal I can't get at&t service they want a huge deposit i think because my student loans are still not paid off anyway. I am leaving Sprint and I want to go to t-mobile can I unlock/jailbreak an Iphone to be fully functional with t-mobile. I want to be able to run the apps like urban spoon shazam etc... So can this be done, I don't care if it voids my warranty with Apple I just want to know if it is possible before I waste my money and get stuck in a contract with t-mobile