Bad power steering pump?

[Mr. Pockets]

So, now that the car is running again, I get to find out all the things that I couldn't when it wasn't. The power steering pump makes a horrible whining/grinding noise when I first start the car and when I turn the steering wheel. The assistance feels...chunky, not smooth.

I assume I need a new pump. Being an LS-L, my car has the speed-sensitive assistance. Do I need to be concerned when I go to Advance and buy their cheapest remanufactured pump? Honestly, I have no idea how that variable assistance works, but I assume the pump itself has nothing to do with it.