It is an A. O. Smith model no. C56M2R4/ 1.5 hp/ 3450 rpm. It was apparently sold by Sears back in the day.
The number you have given is a motor part number and doesn't identify the pump.
We need the following information:
What type of pump? It is probably a shallow well jet pump with one pipe going to the well. If there are two pipes going to the well it is a deep well jet pump. A picture would help.
1. How much water (gallons per minute) do you want to pump?
2. Is this occasional watering from a hose, or do you have an irrigation system? One or more hoses on sprinklers to run for extended periods unattended should be considered an irrigation system.
You can check your water demands by using a hose (or hoses) off your municipal system. Run it at a rate that you are going to want from the pump and check the flow rate using a 5-gallon bucket and a watch to determine the flow rate in GPM.
A 1.5 HP pump will provide a lot of water and is too large if you are only going to use a small flow rate. If you get a more modest pump you can keep the pump from cycling on and off while you are watering.
Many 1/2 HP pumps are pressure limited so you want to verify that such a pump will meet your needs.
If you are doing irrigation you will want to size the pump and irrigation system so the pump will not cycle on and off during extended watering. That can usually be solved with a jet pump by increasing the shutoff pressure on the pressure switch and putting enough hoses on the sprinkler system.