Normal PSI filter ?

[Poconos]

There is no 'normal' pressure. Too many variables. Pump size, filter, pipe diameter and length of runs and so forth. Priming shouldn't take 10 minutes and pressure should stabilize once all air is out of the system. You can see any air in the pump basket and this should blow out in a couple minutes at most. Your normal pressure should be just after cleaning. Unless you're vacuuming I can't imagine any significant amount of dirt getting into the filter that quickly. I know nothing about cartridge filters but can you run the system without the cartridge in place and see what pressure you get then? Would give you an idea how much the filter cartridge itself is restricting the flow. Sorry I couldn't be of more help right now.
Al

[waterbear]

The pressure after the cartridge is cleaned is probably the best to go with. I have a pentair free and clear 150 cartridge and a whisperflo 1.5 HP uprated pump and my normal pressure (since the pool was built and everything new) is about 20 PSI.