Unfortunately, none. CDMA phones (Verizon, Sprint and their virtual network operators) can only be used on the network of the carrier they were sold to. (It's not a technical issue, it's a matter of the carrier, like Sprint, not accepting a phone made for another carrier, like Verizon, on their network.)
As far as using it on AT&T or T-Mobile (or one of their virtual network operators), that would be like expecting to see TV pictures on a radio - the technology, CDMA vs GSM, is just too different to be able to convert one phone to the other technology without, basically removing everything in the case and replacing it. (Except for those phones that do both CDMA and GSM, which the S3 isn't.)
Unless you want to move to one of Verizon's virtual network operators (like Page Plus, Straight Talk, Net10, etc.), sell the S3 on
Swappa and buy a phone for the carrier you want. (Moving to, say, Page Plus, gives you a different plan, but you're still using Verizon's towers.)