Before getting rid of my PS2, I used Retroarch for convenience. It worked well for lighter platforms like Game Boy, Master System, Mega Drive, and NES.
I know there were some decent GBA emulators (GPS2 Kai, TempGBA), but I don’t remember if certain heavier games had issues—wouldn’t be surprised if they did.
SNES already runs with problems no matter which option you use (Snes9x 2002 core, SNESStation, SNESticle...), so it's best to keep expectations low.
For PS1, POPStarter is compatible with about three-quarters of the library, but some big titles don’t run. What discouraged me the most was dealing with its specific settings and formats. The best option is still using physical discs.
In some cases, you can also rely on officially released collections. Companies like Capcom, Midway, SNK, and Taito have re-released many games for the PS2.
Overall, it’s a very limited system for emulation, and you can’t expect miracles. I remember watching a Brazilian YouTube channel about the PS2 homebrew scene, and many people in the comments were hyped, thinking heavier system emulators would eventually come out. Reality is, the PS2 has a pretty low ceiling for this. If any console of that generation stood out in emulation, it was the Xbox.