Re: Unlock iPhone 5
There are companies that will sell you that service. There is one that several of us have used successfully. You can find them on a different thread here about unlocking. Unlocking the phone won't be your problem.
Your problem will be which phone to buy in the U.S. The AT&T phone does not have LTE bands for countries other than U.S. and Canada. The Verizon phone has more international bands but perhaps not the ones you will need. The "world" phone version is not out yet and is specifically intended for use in certain parts of the world with the LTE bands it services. You should look at the LTE bands for each of the 3 different versions of the phone to see which one serves you the best.
Your other problem is that unless you pay the full price for a non-contract phone from AT&T or Verizon you will have to pay 2 years worth of monthly contracts. I'm not sure they would even sell you a phone under contact unless you have a US address. So if you're going to pay full price for a non-contract phone you won't have to worry about unlocking it. It will already come unlocked.
This gets you back to deciding which version of the phone has the LTE bands you need..