Retroarch. And if you want it to look a bit prettier use daijisho as your launcher.
Is there a bsnes/higan core for retroarch on Android?
If I remember correctly, yes. The play store version is a bit outdated though. Use the APK from the retroarch homepage and choose your cores with the internal core downloader.

It depends on the hardware you’re running it on. snes9x is the “accurate enough; runs fine on a potato” option. Bsnes is the “slightly more accurate at the cost of potato performance” option.

If you’re not sure which to use, use snes9x.