Some Rules of Thumb
Every week, you'll need 1 gallon of water for every 2 square feet of annuals or turf that you want to irrigate. Natives need much less.
Every week, your rooftop can collect about 1 gallon for every 2 square feet, on average in Georgia.
The problem is, we don't get the same amount of rain every week, as you know. So how big a tank is ideal? It's a tough question to answer, since one part of the equation is predicting the weather for the next 10-20 years. Another part is predicting water rates for the next few decades. And finally, we need to predict watering restrictions and the outcome of the multi-state "Water War."
We have a modeling app, based on expected demand and rainfall rates. But a quick way to size the tank is to collect FROM a square foot of rooftop for every square foot of annuals or turf we want to irrigate, and size the tank for 1 gallon/square foot collected.
Your rainwater system will cost about $4/gallon installed, plus the piping to route the water to the tanks, and an irrigation system to distribute the water. Add another $2/gallon for underground tanks.