As JL said, look at your pump curve and pump data sheet, most manufacturers will now provide a continuous minimum flow. If it's not on the documentation, contact them.
I assume you'll be measuring the pump discharge flow rate. As you feed more forward to the process or wherever it's going, you need less flow through the bypass to keep the specified minimum flow through the pump.
The minimum flow thus becomes your maximum sizing case. There really is no normal or minimum flow (IMO) since depending on your process, the required minimum flow to keep the pump at its vendor recommended minimum can go all the way to essentially zero and no valve can be sized for an infinite turndown. Which is why you don't want to oversize your valve, performance on the low end will suffer. This is one case where I'd be happy if the valve was almost wide open.
Now, if your pump's minimum flow and process requirements are such that you will always usually be recyling, one could call that the 'normal' flow through the recycle valve but that would be unusual.
For the inlet and outlet pressure, that depends on your system. The dP is the pump head at the minimum flow. If you are taking suction from a tank, the outlet pressue can vary from the correponding value at minimum level to maximum level. I always want to check the valve operation with the tank at minimum level for cavitation. If the dP and vapor pressure is high, you can have cavitation issues. That can be addressed with speciality trim like Cavitrol but you better have clean fluids, they make a great filter.
