I have been using my Galaxy S3 from Verizon Model Number SCH I-535 on Straight Talk for the past 1 Year. No issues at all.
Talk works,
Text works
SMS works
MMS Works
All features works, both I can send or receive SMS and MMS and Picture Messaging and Calls
But Data is limited to only 2G or EDGE, because frequencies are not supported. But other than that, everything should be fine.
With Android 4.1.2 update released on Dec. 12, 2012, Verizon made the SGS3 a global phone, which means, no unlocking required at all. Aftre You update to 4.1.2 stock ROM also, You can still use the GSM SIM cards.
I did use Simple Mobile, before I moved to Straight Talk for Good. Got a 1 Year card. No issues at all. Of course data is one more issue.
If I were You, put a ad in craigslist, and exchange Your SGS3 with that of a T Mobile or AT&T SGS3 and then, Use it, to get the best data speeds as well, since You were planning to move out of verizon for good.
But data limit for AT&T is 2.5 GB LTE but for T-Mobile it is unlimited but the coverage is a big problem. Please check Your local coverage.