SNES is in my opinion, the best way to first experience the game. Either download the ROM or get it on eBay if you have the money. Despite having a sometimes wacky translation, it's charming and has superior sound quality compared to the PSX and DS. Chrono Trigger never needed any changes or extra content to be more perfect from my standards, this is the version to play.
Avoid the PSX version. It's haunted by sound quality worse than the DS, terrible anime cutscenes, and tons and tons of lag. Plus, a fourth composer translated every single song from the SNES over from memory, resulting in lots of missed/wrong notes. Plus, the PSX and DS can't render the SNES synthwaves correctly, as a result they butcher the Undersea Palace, Zeal Palace, and Last Battle themes.
DS is the best remaster/port of the game, but the lower sound quality, poorly designed Lost Sanctum, and rehashing the cringeworthy cutscenes and force-feeding you them when you turn the game on even if you turn them off in your save file all hurt.
Mobile is alright, but lacks any of the extra PSX/DS bonus menus, has a strange text font, forces the anime cutscenes (but you can skip them), and was retroactively given the smoothing steam filter over everything.
The PC version still has some gameplay-hindering bugs, has some of the extra menus but not all of them, copies the DS font instead of using a more readable/nicer looking one, and force-feeds you the terrible anime cutscenes.
From worst to best, PSX, PC/Mobile, DS, SNES.