I'm interested in buying a good used car that's good on gas and won't cost much to insure. I was told to buy Japanese because American cars always fall apart. I admit my ignorance here. Help?

Toyotas and Hondas are justly famous for reliability.

I'm on (I think) my 5th Toyota. The Camry I'm driving now was born in 1993 and has never had major work done on the engine or transmission, it crossed the 200,000 mile point last month, so I bought it a cinnamon bun and ate it myself (it has no mouth).

I got my first car over 30 years ago. I dreaded getting a car, since all the Detroit models I grew up around were always in and out of the shop.
I got a Toyota 1200 and the thing ran without trouble. I have since averaged 8 years and 187,000 miles per vehicle, which have included Toyota, Nissan, and now Honda. All three have production facilities in USA. The distinction of "American" and "foreign" is largely political now. For example, all vehicles have microprocessor and integrated circuit components, which are all made offshore.
If you wish for a neutral source for reliability evaluation, see if your library has back issues of Consumer Reports. If you check consumer reports online you have to subscribe.

If you go to consumer reports there is a section that breaks down good used cars by price. I would check that out. Reliability is a big part of how they choose these cars.

In my life I've owned 8 vehicles. A VW bug that did quite well, and a Volvo as a second hand car. The rest, even the second cars, were Toyota. They are tanks. They run forever and need virtually NO work. Best cars on the road.

The best cheap car that was best on gas that I ever had was a Mazda 323.

I've had several cars since but I am back driving a Mazda now. I love it!

Honda is famous though for their reliability. They'll last you forever.