That's about it. You need a GSM based device for use on T-Mobile's network. Grab either an international version, or ATT's version of the S3 to at least get the ball rolling. Always check GSM arena (etc.) for the specs. Go here-
I have a Samsung Galaxy S3 for Verizon. I have rooted it and unlocked the bootloader. What would be my next step to get it to work on TMobile?