Yea sorry guys, mea culpa. The other posters are correct: Technically you DO need an unlocked bootloader, but yours came out of the box already unlocked, so you're good to go. Only those of us on Verizon had locked bootloaders originally. I took the text from the Verizon OP and pasted it in here. I tried to scrub any references to Verizon, but looks like I missed some - cut me some slack, it was 2 AM
Also, as for multicarrier support, please read this post by our team's TrevE. Use whatever ROM you like (you won't see me in here telling you which ROM to use or trash-talking another ROM), but you should at least be advised that most other multicarrier ROMs out there for the both international and US S3s are missing some important code. If something goes wrong you can trip EFS codes that write so low-level that you could end up failing a bench test if it came to that:
http://xdaforums.com/showpost.php?p=37069815&postcount=15664
SynergyROM patches these files correctly for proper multicarrier support so that you don't have to worry.
.....
Finally, those of you with wifi issues: Which kernels are you guys using?
Try a couple of different kernel combos during install so that we can pin down what works and what doesn't so that we can get you guys rolling ASAP.