You seem like the same exact Smartphone user as I am. Ultra-basic. I don't even come close to 2GB.
If you were on Verizon, I don't believe your phone would work on T-Mobile. You would have to get an S3 for the T-Mobile network. For example, as someone who uses Wal-Mart Family Mobile (which is basically T-Mobile), I can only use AT&T and T-Mobile phones (though, certain "world phones" may work across all networks - I'm still foggy on this).
Therefore, I do think you could use that Verizon S3 on Straight Talk. I'm a little less sure here, try this link and report back:
http://www.straighttalkbyop.com/
Btw, S3's go for $299 or less, brand new, these days. Hence, the insurance seems like a waste of money (especially when you consider your $100 deductible and monthly charges).
EDIT: Check out this link too. Lots of good info and it's similar to your situation (he's switching from Verizon to T-Mobile, and he's based in new york). You may be able to get value for your phone straight from T-Mobile:
http://www.businessinsider.com/t-mobile-switch-2014-1