Cam,
I'm taking a guess that this is closely linked to your previous post - here for anyone who wants to check it out -
-. For me I think you need to first work out what you want the flow to do and then choose an appropriate pump rather than try and choose a pump for an unknown duty.
From what I can gather you want to have 100 psi in a no flow situation, presumably as a pressure differential, i.e. 0 psig on the far side. Then you want to open and close the valve lots of times. However it is unclear if you want a certain flow through the valve before it closes or what. It would be very good for you to think about the flows and pressures in this period.
The issue is that if you dead head a pump then open the discharge but to a very low pressure drop you would get a v high instantaneous flow before it decays to the steady flow the pump is capable of. These are the properties of a PD type pump, but I would choose a pulseless type such as a gear pump or similar, not a diaphragm unit or similar which is highly pulse driven. You need a fixed flow through the pump and with a pressure relief valve this can be established and then flows through your valve before you turn it off again.
Alternatively have an accumulator and d/s of the valve introduce some sort of restriction (orifice, control valve etc) such that the flow rate is limited once your valve is open. An open pipe back to the sump tank would provide only low pressure drop and hence potentially very high flow before you turn your valve off.
When you work out what sort of flow and pressure you want across the entire on/off cycle then you can find the right pump.
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way