Chrono Trigger will always be one of my all-time favorite stories on any medium.
A few other SNES recommendations from the top of my head:
• EarthBound (aka Mother 2, another popular RPG with fun music. Combat may feel too grindy/frustrating though)
• Super Gussun Oyoyo (Lemmings + Tetris)
• Live A Live (RPG where you play characters from multiple timelines)
• Pop'n TwinBee (shoot-em-up and platformer with very colorful graphics in a pastelly palette)
• Terranigma (RPG spanning multiple eras)
• Treasure of the Rudras (Japan-only RPG with fan translation)
• Bomberman (hilarious couch PvP)
• Pocky & Rocky (cute shoot-em-up with a Japanese folklore theme)
• Yoshi's Island (one of the best platformers)
There were a bunch of other obscure titles with unique gameplay mechanics that I can't recall the names of at the moment. Will have to comb my ROMs folder.
I really want it on the Switch! I played the emulated version on PC, and I know it's now available on both Steam (I heard that they fixed the broken early version) and mobile, but it would be very convenient to have it on the Switch. I read that due to licensing it's unlikely to show up in SNES Online, but I don't see why they don't release it as a separate game.
They don't need to remaster or remake anything, just release it as is, and I'm sure it would sell well. I would anyway prefer the original with original graphics and soundtrack to a 3D remake or similar.
The DS version is an excellent port - much better than the Final Fantasy ports to the GBA, because they didn't have to compromise on the resolution. It's selling for about $55 now.
(Yes, I know this is quite different than having it on the Switch, but I mentioned it in case you have a DS and wasn't aware.)