If I need to adjust both derailluers, I should begin by adjusting the rear derailluer first, right? I’m thinking I can’t get the spacing correct on the front until the rear is tracking correctly.
You should probably start with the rear derailleur. Since you’ll need to have the rear derailleur shifted into the smallest and largest cogs to set the limit screws on the front derailleur (to keep the chain from rubbing the front derailleur cage), it’s best to get the rear sorted out first.
Park Tool has a simple but effective rear hanger alignment tool. The hanger gets banged around over time and straightening it up makes a world of difference. I’d been chasing the rear derailluer adjustment since I got my bike from a CL seller. It was never quite right. Turns out the rear hanger was a good 15 degrees off. Once that was straightened out it shifts like butter.
Thanks for the tips. Turns out most of the problem was in the rear, and getting that right took care of most of the chain rub on the front, with only a few tweaks needed. Since I don’t have a proper workstand, I had to suspend my bike from the basement ceiling joists with ropes tied around the seat post and handlebar stem. Not the steadiest platform, but I made it work.