The ease of connecting at Hartsfield depends a great deal on the airline that you are using.
Domestic flights arrive and depart from any one of 6 concourses -- A, B, C, D, E, and T. Each concourse has maybe 25 gates.
If you are flying Delta, then you really have to allow more layover/connecting time. Because Delta has such a large presence in Atlanta, they use gates in probably 5 of those 6 concourses. So you might arrive at A and have to connect to a flight at D.
Southwest has a smaller presence in Atlanta, so their gates are confined to just a couple of concourses. Looks to me like it's C and D. You would have less possible territory to have to cover to go from one Southwest gate to another Southwest gate.
It also always works in your favor when your connecting flights are on the same airline. They know where their connecting passengers are coming from, and they do all they can, within reason, to wait for you to make your connection.
So, to the OP, your original option that involved a 1 hour Atlanta layover, with both flights being Southwest, would in all likelihood work just fine.
Connections that involve an international flight are altogether different. There is a brand new international terminal that is a bus ride away from the domestic terminals.