Once I have the boot loader on I then can just put the chip in my uno and program it from there can I not?
Yes
Also does it matter that it's an Atmega328-PU? The one that's in my uno is an Atmega328P-PU
I believe it does matter and that you would have problems trying to burn the bootloader using the arduino as ISP sketch. However there is a solution as user westfw has created a sketch called optiloader that once loaded onto your Uno board and wired to your standalone 328 chip will transfer the bootloader correctly. Then those chips will work when installed in the Uno board.
GitHub - WestfW/OptiLoader: Arduino sketch for burning new bootloaders
Lefty