Bsnes/higan/ares. These three came from the same Dev (rip byuu/near). Not sure which one is the best, I'm a little lost in the history of them. Maybe Ares if you want easy of use.

I swear I had a Japanese version (Super Famicom) with better hover cars back in the day although my memory is shaky about it.

Are you thinking of the more detailed vehicles from BS F-Zero Grand Prix 2 perhaps? If so, they can be added to F-Zero with a ROM hack. As explained here, you can also apply a MSU-1 patch on top of that for CD quality music in any emulator that supports it (i.e. ares/bsnes/Mesen/Snes9x).

I use RetroArch for everything 16-bit and older these days (unless there's no RA core for the system on the platform I'm using). Haven't played SNES for a while, but I have been using the SNES 9x cores. For most games you can just use the most recent core, but there are a handful of games that work better with one of the older cores.

The first F-Zero I played was the GBA version, which I also recommend.

Any emulator should be fine. I use https://retrodeck.net/ and it's OK so far.

Project64, ares (I know this one is windows only but it covers a lot), and I think you can play f-zero on the browser too. https://vimm.net/ might have it (Vimm's Lair) but Nintendo hit them a bit ago with some takedowns.

Dolphin Emu has always been reliable for emulators. I emulated Pokémon red on my android