First, let's begin with the common terminology you'll see when researching pond pumps. The flow rate is measured in gallons per hour (GPH) and means exactly that - the number of gallons the pump will push in an hour. Pumps designed especially for ponds will be labeled with a GPH rating. But note that if you are considering using a pump made for pools or spas, these will typically be rated by GPM or gallons per minute. In that case, you can do a simple conversion by multiplying the GPM rating by 60 (the number of minutes in an hour). So a 50 GPM pool pump would circulate 3000 GPH.
Shut-off height is another term you'll see which refers to the maximum elevation a pond pump will still pump at. This is important especially in waterfall applications where water must be pumped upward. You need to make sure your pump's shut-off height will match the height of your waterfall.
TDH or total dynamic head is a measurement of the resistance to flow. Your pump will be rated at a certain GPH flow rate but you have to remember that each pond installation can be very different in terms of the length and size of plumbing, elevation and other factors. As the pump pushes water through the pipes, that flow will encounter resistance or pressure. An example of this would be a 90 degree plumbing elbow - water will be flowing along through straight pipe and then suddenly hit a right angle; this will decrease the flow regardless of what GPH rating is on the pump. TDH accounts for this and basically provides an honest assessment of your pump's output. Since there is some math and equipment used in calculating TDH, this is typically calculated by a professional pond installer.
Now that we've covered pond pump basics, consider the flow rate you'll need for your pond. The experts' rule of thumb is 1500 GPH per foot of waterfall width (the width is measured at the initial waterfall drop).If your waterfall is 2 feet wide at that point, then a 3000 GPH pump is suggested by this general guideline. But keep in mind, as mentioned above, elevation and resistance will reduce that flow rate and must always be taken into account. You want a flow rate that gives you the right balance of water (not gushing and not trickling).
As for plumbing, it is best to check with the manufacturer of your pond pump for their recommendation. That being said, flexible pvc (also called flex pipe) is a favorite for ponds. Due to its flexibility, it can curve as needed to accommodate turns and small spaces. The material also handles expansion and contraction caused by changes in temperature.
The final component is a check valve to prevent back flow of water. When your pump is turned off, either by choice or power failure, water will flow backwards into the pond. But you really want this water to stay in the biological filter to nourish good bacteria. So be sure to include a check valve when choosing your pump and plumbing.