In regard to check valves, you simply use the flapper style ones as they pose no resistance on the flow of water. What you want to avoid is spring check valves, as it requires substantial water force to keep them open.
Koiguy is absolutely right and you do neet a checkvalve right after those barrels so that you don't have all that water backsliding into the pond. If you can afford it, buy a clear check valve with two unions on the ends, as if you ever get anything stuck in the valve, you can clearly see it and then unscrew one of the unions to separate the pipe so you can get at the clog without havine to saw through your pipe.
It's very important to incorporate a few unions or rubber connectors in a few spots in your system so you can easily remove sections of it in case of a problem.