It costs like $10 or something to efile with the state depending on the software/company you use. Some places will do it for you for free, but you have to shop around to find the best deal. The fee goes to the e-filing company, not the state.
You can pay with either CC or E-Check.
When I used to pay by check, Georgia always seemed to take 6-8 weeks before cashing it. Feds would cash it within 2 weeks usually. I guess they just want your money faster. Hard to believe Georgia doesn't considering the financial shape the state is in right now.
techfuzz