You need the ST AT&T sim to use the BYOP service that they offer (or were offering) for AT&T locked phones. While they have stopped selling the AT&T sims you can still activate if you have one. A couple people have activated the ST AT&T sims in the last couple of days they still work. WM.com had the standard size still for sale (last I knew). People on Ebay and other private sellers have either available. Right now they are no longer available on ST website and they've removed all reference to ATT from their website. It's all Tmobile now. The phone availability that use AT&T are is also gone (at least when I checked for my zip).
I'm planning on likely using the S3 on ST ATT myself. I've looked heavily at a few different phones. S3 seems to be the one I like best. ATT is better than TMobile for me. I planned to just go ahead and get a carrier locked ATT phone.
ETA: Just checked on the WM.com site, they now have the AT&T ST micro sims in stock again. You want to order that to use with your S3. Still not on ST site and it only says TMobile for everything and bring a TM or unlocked phone. It does still say this at the bottom of the page "Straight talk SIM Card will only work with an AT&T or T-mobile compatible or unlocked GSM phone." But they are not selling the sims or advertising it on their site. WEIRD.