1. I know I will have to submit taxes for GA in 2020 because I will have rental income. I have no rental income in 2019, but do I still have to submit taxes in GA because I actually purchased the home in 2019?
Based on the information you have provided, you have no need and no reason to file a 2019 GA state tax return. Only a federal return
2. Since I purchased the home in 2019, can I deduct anything this year that I paid as part of the purchase (prorated interest, taxes, etc.)?
You will deal with "EVERYTHING" concerning the acquisition of the property on your 2020 taxes next year. Both your 2020 federal return and what will be your first 2020 GA state return, as well as a return for whatever your resident state is, if your resident state taxes personal income.
3. I traveled to GA, installed new appliances, and made some repairs to the home in 2019 immediately after purchase to get it ready to list as a rental. Can I deduct these costs since they were accrued BEFORE the home actually had its first renter?
No. When you initially acquire rental property, repair and maintenance expenses incurred "to prepare the property for rent" for that first time, are just flat out not deductible. But if your "repair" costs aren't to excessive, add them to the cost basis of the appliances if the "repair" done is someone related to the appliances.
As for the appliances, those are rental assets. However, if they cost less than $2,500 you can expense them (and I recommend you do) under the Safe Harbor De-Minimus act. But you'll expense them the year placed "in service" which means you can do so on your 2020 tax return.
As a final note, if you drove from CA to GA for this, then I recommend you "NOT" claim vehicle use for this rental. In the long run it won't be worth it and will create a potential tax filing nightmare (Fed and GA state) for you in the tax year you sell or otherwise dispose of that vehicle.
If you flew to GA for the primary purpose of buying/installing appliances, then include your airfare in the cost basis of the appliances. Of course, if that makes the cost of the appliances more than $2,500 then you have no choice but to capitalize and depreciate them. Most likely though, you'd still be able to take the 50% special depreciation allowance the first year they're placed in service. (Though I don't know why you'd want to take that special allowance, since doing so will not make one single penny of difference in your tax liability)
