I’d recommend a cheap USB GameCube controller, you can probably get one for less than $15

If you plan on eventually switching to NTSC, I would recommend that you don't spend a whole lot of time practicing and learning a run on PAL. Once you're used to PAL's 25 FPS, NTSC's 30 FPS seems ridiculously fast. (Speaking from experience)

I'm pretty sure Mupen64plus is an acceptable emulator/core, I don't see why different front-ends would make too much of a difference in terms of how it performs

Doesn't mean you can't learn on mobile, but you'd have to use something like PJ64 to actually submit runs