NormL, if you have a PTO pump, hang on to it. A PTO pump is worth a bit more than the smaller pump you'd need considering the RPM's you can run with your garden tractor. Does the moco have a pump on it? Most pumps are rated by cubic inches per revolution. For example
this pump from Surplus Center is a 0.49 cu. in. pump. If you run it 1:1 with your garden tractor engine at 3,000 rpm you get 1470 cu. in./minute or 6.36 GPM. (231 cu. in./Gallon) To get the same flow from a 540 RPM PTO pump you need a 2.7 cu. in. pump (or gearing to speed it up).
As far as single acting vs. double acting, a pump is always single acting (it always pumps fluid in one direction). It's the valves and cylinders that can be double acting.