There is no "priming", we changed mine this spring (the old one was seeping gas thru its seams".
The car fired right up. Get a pressure test kit and, as DJ said, find out what your fuel pressure is.

This one is what I have, fits my Crossfire and my Ford Ranger:
https://www.summitracing.com/parts/otc-5630
Makes it as easy as checking tire pressure - the spec is 58 pounds +/- 3 pounds.

You should know that our cars do not monitor fuel pressure, so it can be bad and the ECU does not know it.
But since you said you changed the pump and it wont run, you either got a bad pump or you plumbed it wrong. }
Well, that or the filter/regulator is bad, IF this is fuel related. But you know NOTHING if you don't know your pressure.