I recommend using flow rate not HP as the basis for your choice. More HP does not always equal more flow rate - but it does equal using more electricty!
Your pump should turn your water over at least once per day (twice is better, three times is wasting electricity). By "turn over", I mean equivalently filtering all of the water in the pool. In your example, you would like the filter to clean between 10,000 (one turn) and 20,000 (two turns) gallons per day.
Therefore, to accomplish this in 8 hours (480 minutes), you would need a pump that flows 20.8 gal/min for one turn and 41.6 gal/min for two turns.
I am sure that you can find a good, reliable pump that flows in that range in a 3/4 HP model. (Some 1/2 HP models may also meet this requirement, but would probably be near the top limit of their flow rates).
You did not mention anything about height changes in you plumbing, but if you are pumping water up to a solar heater on the roof or other vertical distance, then that pressure loss would also need to be considered in the selection of the pump. Also, you need to consider special filtering requirements and/or other pump/pressure needs (spa, etc..).
The goal is to match the flow rate to your pools needs without wasting electricity.
I would add that you have to match or take into consideration the flow rate, size and type of the filter plus the heater max. flow rate to get the proper GPM in a totally balanced system.
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