So, I'm kind of interested in CD-i runs in general, but I'm a bit lost as to which one to use (to say nothing of actually trying to get ahold of the console itslef).

Is there one generally accepted for Hotel Mario/CD-i runs in general?

Emulators are indeed allowed! It's a separate leaderboard since the emulators aren't too accurate (they are a bit faster than the OG hardware), but it's a great way to get started.

The most recent MAME version has improved compatibility with the CD-i quite a bit, so I'd suggest to start looking there. Sadly I'm not well versed in MAME or CD-i emulation as I'm lucky enough to have the hardware, but it can get you started :)