I currently am using an LG phone with TMobile domestically in the U.S. I plan to give my current phone to sister, thus I am planning to buy an Iphone 5s on Ebay. I noticed they had a few options like GSM unlocked, TMobile, At&t, Verizon, etc to choose from in addition to color and memory(16g or 32g).

So my question is, should i get a GSM unlock since that should take care of not having to contact Tmobile about unlocking the iphone when i travel to Europe and also being able to use at home since it should work abroad and home. Or should just get the tmobile version and just let tmobile unlock it when i go to Europe and buy a local sim card there for use ? Or if i choose to use tmobile's plan, i don't need to call them at all since they have coverage in most parts of europe anyway.

I basically want the version that i can use in Europe and domestically(U.S) without hassle. Thanks.