As far as Chrono Trigger goes I would have to say the SNES version would be the best bet.
As far as the script goes, I'm pretty sure both the PSX version and the SNES versions are the same.
The PSX version has animated cut scenes at certain parts of the game which is nice, but the load times for the PSX version are horrible. I'm not sure if the emulated version has the long load time, but I'd say to be safe just play the SNES one. You can watch the animated cut scenes on Youtube if you really want to, they are nice, but not crucial to the story by any means.
If you really want the best Chrono Trigger experience, play the Japanese version and learn Japanese
, but if that's too much(I know it is for me lol) we are working on a retranslation project currently. When I say we I mean people at the Compendium. I know they are almost done with that, but it might be a little while until they match a playable version of that script.
Well, I hope I didn't confuse you with this long post. To summarize, right now I'd go with the SNES version and watch the cut scenes on Youtube.
As far as FF6 goes, I'd say go with FF6 advanced. I hear it's more true to the original Japanese script, has 4 extra Espers, and I'm pretty sure it has a new dungeon.
Welcome to the Compendium, and I hope I helped ya out a bit. Heres to more interesting topics about the Chrono Trigger universe.