The best shoes to wear to clog in are the most comfortable flat heeled, hard-soled shoes that you can beg, borrow or steal. It is good to have a lace or a strap for security.
After that it is a matter of taste, some people wear plain taps toe and heel, others wear echo taps - a tap and base plate that can be adjusted to make a louder sound, or other kinds of taps such as rattlers like Stevenson Stompers or Freed's Jingle Taps, some have metal tips put on by the cobbler, and some superglue taps onto trainers.
Some Old-Timey musicians HATE cloggers with taps on their shoes but taps can make dancing for long periods of time much easier on the knees. Cowboy boots and lace up boots are great to dance in. A local dance supply shop will be able to supply taps or order them from Freed; they too will probably be able to recommend a cobbler who will fit taps.
Tap shoes don't seem to have the right feel about them for clogging, a pair of brogues or boots feel much better or a pair of character shoes.