I have the Shimano M324 pedals and I like them. I like them very much. Not too expensive as pedals go and do exactly what you are wanting--clip in on one side and wear regular shoes on the other. The pedals will come with the cleats that attach to the special shoes.
You will need "mountain bike" shoes--also called SPD shoes. They tend to be cheaper than the more "roadie" type shoes. Plus, SPD/mountain type shoes are fine for walking around in--ride to the store and be able to walk around to do a bit of shopping. (You would not want to walk very far in dedicated road bike shoes!)