There is a wide range of American Flyer transformers available from throughout the years going back to WWII. Smaller ones have less power and fewer features. Larger ones have more power and features. A set this size can be very enjoyably run with a transformer at the smaller rather than larger end of the spectrum.
The best thing to do is find an American Flyer guy (person?) who can advise you on an economical and yet good choice for your train set. There are a ton of these guys out there. They are most often friendly and helpful.
Maybe someone in our club knows. But, failing in that you can do an Internet search or go to a regional train show and find one.
Good luck.
Bill