I finally got myself a pair of Nomex racing shoes a couple years ago. Before that, I always used a pair of Converse Chuck taylor All Stars. The wide flat sole makes it easier to heel-toe and the smooth sides do not have any overhang to catch under adjacent pedals. Also, the flexible sole gives excellent brake feel. Keds would also serve well as bargain driving school shoes. Either way, you can find a nice pair for under $30. I usually wear Chucks when I autocross because I feel kind of silly wearing racing shoes in a parking lot.
I suggest staying away from walking, work, or dress shoes. These typically have a sole that projects past the upper which makes it very easy to catch under a pedal.
Ed