Default [Q] Tmobile Samsung galaxy s3 which model?

This is driving me crazy. I have spent the last 3 days trying to figure out which model to get. I want the best speed available. I assume that is LTE 4G. There are too many models available. It is too confusing for me and calling T mobile is useless since none of their employees seem to know what is going on and so far 4 different employees have told me different things.

I am buying an UNLOCKED Samsung Galaxy S3. I want the freedom to be able to use any carrier I want when I want. I am in the US. Apparently not all the models of the Galaxy S3 have 4G LTE capabilities. Which model has it please tell me. I just want to buy a phone. I never knew it would be this difficult.

GT i9305 SGH T999 i535. i747. i9300.

If I use Tmobile I want the LTE 4 G. the fastest internet possible.

I am buying the phone on EBAY listed as UNLOCKED

please help me