Unlocked is the state of the phone. The phone could be handed to anyone out of the box and work with every carrier. If you're still on a contract with a carrier, you can't leave without paying a ETF, but your phone won't be stopping you.
AT&T is kinda an oddball this year, I don't know if their device got CDMA certification. The hardware is capable of working on Verizon, but I don't know if it actually will. Any other carrier's iPhone will work with all carriers, it'll be missing some AT&T optimization, though.
Edit: also note that since you're paying full price, you don't have to buy the AT&T model. You can just buy the T-Mo model and use it on AT&T, and then switch to whatever carrier you want after.