I think all we know is the SG3 will be released sometime, somewhere, and somehow in the US. When and what carriers remains a mystery.
That said, it does seem reasonable that all 4 main US carriers will get the SG3, hopefully at the same time. Date of release to be announced in June, but I would not be surprised if it was not in US hands until later.
I believe that AT&T was the application that was approved on May 14th.
Accessories for the AT&T and TMO variants have hit Amazon as well as SIM-free units for $799. Betting AT&T prices the SG3 at $299 for 2 year contract. This would be a bit higher than their usual smartphone pricepoint. Is the customary for Android devices?