Use whatever control you like.

Most people use either an N64 controller or a GameCube one. But it’s not like there’s any rules against it. Any controller will only work as well as the adapter you use (or how well the Bluetooth is picked up for PS4 controller) as well as how good your computer is at running the emulator.

I run Mario 64 (badly) and use a PS4 controller, don't feel like I could go significantly quicker if I had an N64 controller so I would say for beginner runners you definitely won't lose out using a non-optimised controller.

Use DS4Windows and set up your controller on that so you can use it wirelessly and then just map in Project64.

I find using R2 for Z and the right stick for the camera buttons (never owned N64 so not sure what they are called) works well with everything else mapped to the obvious buttons.