the difference between biking shoes and walking shoes is that walking shoes are made to support your foot as it makes an impact going down. biking shoes are made to support your foot as it exerts force spinning through a circle. more like a glove than a shoe.

that said, you might or might not need your stiff, custom made arch supports. you may or may not be able to fit them in the shoe. experience will be your best guide in this situation, so i recommend going to a shop to shop for shoes and bringing out supports with you.

when i worked in a shop i heard lots of people talk about knees and clipless pedals. some people loved the lots-of-float (side to side movement) that Speedplay allowed, and others found that less float, from more standard pedal designs, was better for their knees, because it focused the movement on the spin and allowed no haphazard side-to-side.

again, experience is going to be your guide.