Since Chrono Trigger is my favorite game of all time I can not recommend you play the PSX port first. I originally played it on SNES, then when the PSX version came out I endured the crap (you have to wait a good 10 seconds every time you open up your menu, close your menu, and enter a battle... it's bad) to see all the new stuff, but I would consider myself pretty patient when it comes to video games. However, the DS port exists and is the best version of the game, hands down.
I say, if you have no other option, play it on playstation... but if you can help it play it on Super Nintendo or preferably Nintendo DS.
Final Fantasy 5 is actually my favorite final fantasy and with that one you don't have much of a choice. Play the sluggish PSX version or play the gba version with poor sound... in which case I choose the sluggish version just for the sound quality.
Check out Racketboy's site for some recommendations. Love this site.
Defining Games:
http://www.racketboy.com/retro/games-th ... tation-ps1Hidden Gems:
http://www.racketboy.com/retro/best-und ... on-ps1-psxAs for my personal favorites:
Mega Man Legends
Suikoden 2
Chrono Cross
Metal Gear Solid
Resident Evil 2
Harvest Moon: Back to Nature
Legend of Dragoon
Hope that helps some and enjoy the PSX. It's one of my favorite consoles of all time.