After going through a few forum posts, I think I’m going to start with replacing some of the capacitors and the 7805 5V voltage regulator on one of the Atari 2600s (the older one).
Physically the caps look fine but after who knows how long in storage, they probably need replacing anyway. There are three electrolytic capacitors, five mylar film (green chiclets) capacitors, two polystyrene capacitors and one ceramic disk capacitor I’m planning to replace.
I’ve replaced the video cord with an RCA-F adapter, so now the video signal will go through regular RG-6 coax right to the TV’s coax/cable input.
The power connector is a 3.5 mm tip-ring jack, which I’d like to replace as well with a more standard 2.1 mm barrel jack, but finding one with the right footprint is proving a bit difficult. That might be a second slightly more involved project.
Time to go shopping in my parts bins. I think I should have most of what I need already on hand.