Well, as far as the sample rates go, the higher the better is in many cases true. However, for the SNES, its original sample rate was 32000Hz, and setting it for that frequency should give accurate sound for less of a cost in speed than 44100Hz (in fact, 44100Hz can sometimes sound off). That said, I'm not sure if the PSP has any specific sample rate that it's "locked" to, like the SoundBlaster Live was (48kHz), and if so, you'd get better quality out of matching that regardless, but I get the feeling that's not the case.
With the Genesis, all of its sound was generated by FM synthesis, so there wasn't really a sample rate as such - Though, usually, 22050Hz is more than enough for the Genesis to sound just fine. In the case of the NES, it was actually able to generate tones up to an incredibly high range, but generally 44100Hz will sound accurate; 22050Hz will sound perfectly fine through the speakers, but will sound somewhat staticcy through good headphones.
TL;DR, in practice, the best thing to do with sample rates is to match the original hardware. If you don't know it, the higher the better.
Mega Man X3 seems to cause major lag with SNES9x on the PSP, and I don't really think there's anything that can be done about that aside from frameskip or turning off the sound. It's just a really intense game.
As for arcade emulators capable of playing those games... I'm not sure.
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