If there's a bike co-op in your area, they may offer classes. And volunteer there if you can.
I agree, flat tires are the most common reason bikes aren't ridden.
Safety of course is most important, so keeping the brakes working and preventing problems should be high on the list.
I see a lot of old bikes donated to a nonprofit I volunteer at, and one of the most common reasons is shifting problems. They can be finicky and annoying and take some experience and money to fix, but aren't as important.