To be totally clear about the keypads themselves: Each keypad is a home-run to the panel? Or do I just have one keypad go to the panel and then daisy chain from keypad to keypad? This will help me determine how much of the 22/4 I need to purchase.
Home runs are best. It's technically possible to connect keypads in other ways (could require larger wire), but you're more likely to run into problems where you might be trying to pull too much current through a set of wires given the distance and load of additional keypads. There's often some guidance about this in the panel manuals.
I'd also probably run a Cat-5e / Cat-6 to the keypad locations for future proofing.
Another choice is whether you put your zone expander in the panel or put it in a closet somewhere closer to the zones you're connecting to it.
Make sure you run some Cat-6 or better cable to various points in the house, every bedroom / office, every tv, and anywhere you might want a wifi access point.
Generally speaking, it seems you have a lot to learn and likely not enough time to do so. Some of the details of the alarm system can be worked out later as long as the wires are run well. I'll try to see if I can dig up some old threads that may be helpful.
I hope you have some sense about this, but try not to do anything too stupid when it comes to actually installing cables; you'd be shocked at some of the idiotic things the previous owner of a friend's house did to run network cables that compromised key structural and fire rated assemblies.