A NAPA pump should be fine. I'd just avoid the Autozone stuff.
On the pump, be sure you get the right one for your year Jeep. V Belt drive run in the opposite direction of a serpentine belt drive.
The system will, over time, bleed itself whether the lever is flipped open or not on the radiator cap. The only thing the lever does is to relieve any pressure built up in the system.
There are a number of different ways to bleed the air out of the system, and each one has its merits. The way I have done it it to remove the return hose from the heater core and run water into the radiator. I put my thumb over the place the heater hose connected to, so the water is forced through as much of the system as possible.
There should be water flowing out of both the heater hose, and its connection. While the water is still running, I reinstall the heater hose. Then run the engine.
I fill the coolant recovery tank with straight anti freeze. If I need to add any more fluid to the system, I use straight anti freeze. Since my Jeep is in Death Valley, and I don't have a concern on freezing, I only run about 25% antifreeze for corrosion protection. I just keep track of how much I add.
David Bricker / SYR