any normal cycling shoe with a rigid sole will do the job but you have to give some a try as the cycling shoes are often apart in size (mostly they are smaller than expected by the size). I would recommend MTB- shoes as it is easier to go with, racing shoes has a slippery sole often. Shimanos are well in quality, price and in size for example.
In fact, I would claim "Jehowa" (you may stone me to death)- for best cycling experience I recommend MTB Shoes with cleats on clipless pedals. If you ever used one, there is no way back as it is much, much better. Really. Eggbeaters or Shimano SPD for example.
All my cycles are equipped with clipless systems except the Pro Mark II (1980 DA Dynadrive) one Meral a dahon Smooth Hound and the other Motobecane.
best regards, Richard