Do you already have a specific S3 picked out? If so, what carrier?
3 of the cheapest services I know of if you want data are Republic Wireless, Ting, and T-Mobile's $30 prepaid 100 min, unlimited text and data (what I personally use). Republic requires you to buy their phone (at least when I last checked), but its not priced too bad. It tries to use wifi as much as possible to reduce costs. Runs off Sprint's network. Ting uses a tiered plan that charges you based on your usage, can be great if you don't use much or have multiple phones on the same plan. You can bring most Sprint phones and it uses the Sprint network. T-Mobile lets you bring your own compatible phone, but to get that plan you have to do a new activation which requires buying a $10 SIM kit from their site. Uses T-Mobile's network, obviously.
All 3 are good providers. It'll come down to which one fits your usage best and has good coverage in your area. Sprint has terrible coverage where I live, so that ruled out Republic and Ting for me. There may be other options now, but when I switched from Verizon a few months ago, these were the best I found.
