The advice I've heard repeated the most for pretty much the same goal that I have (local flying with my kids) was to simply go to a local flight school and get a local area checkout in the plane I'll be renting. My background has enough variety in acft type that I expect it'll be 1 or maybe 2 flights plus an hour or two of ground instruction, but even several visits to the local training outfit would be worth it to avoid all the hazards everyone else has already mentioned.

Same goes with my "someday plan" for getting an instructor checkout in a plane capable of mild aerobatics so I could do some occasional upset training. Get checked out in the plane you want to fly and hook up with a local training outfit to the point where you're good to fly with their existing students. That's one way to get your GA itch scratched while having someone else pay for at least part of it...