I am active duty military with a home of record being Florida. I am stationed in Georgia. Do I need to file a GA return?

You will only need to file in your home state of record. Regarding your wife's income, she would only need to file a resident SC return if she is not covered by MSRRA and her resident state is SC. If she is not covered by MSRRA and not a resident of SC, then a nonresident SC return. If covered under MSRRA, then only files in your state of record (and since FL has not state income taxes, then no state filing is required).

Just make sure that you are letting the TurboTax system know that you are on active military duty and that you are inputting your state of legal residency (SLR) as your resident state. Your SLR is usually your home of record – the state recorded by the military as your home when you joined the military (regardless of where you are stationed).

For example if your SLR is FL but he is stationed in GA, then he will use FL as his resident state in TurboTax. 

If necessary , you may need to edit your personal information under the Personal Info tab (for TurboTax Online sign-in, click Here) to let the TurboTax system know that you are in the U.S. Armed Forces.

You will need to make sure that you select yes -"I am a member or former member of the U.S. Armed Forces (active, reserve or National Guard)".

Also answer "no" to "I lived in another state" (screenshot). Even though you may have lived in a different state, this will not apply if your spouse is on active military service in a state other than your home of record state.

Additionally, if your spouse earned any income outside their military pay in a state that is not your state of record, your spouse will need to file a nonresident state income tax return to recognize this nonmilitary income. Otherwise you will only have a resident state income tax return for your home of record, the state where you lived when you joined the military.