Exactly what kind of pump do I need to buy? Does it have to pump a certain number of gallons per hour?

Pond supplies stores online and in larger cities will carry submersible pond pumps specifically designed for pond use. It is best to know a few things before hand, then contact the supply store with the info you have, and they will make a recommendation. First know how wide you want the waterfall to be (say, 13"). Then know how deep you would like the water at the falls it to be; an inch or two is common. Then find out how much of a difference there is in height from the top of the lower pool to the top of the upper pool, or waterfall exit. The sales person will know what pump can handle that flow and total lift.