I want to play Chrono Trigger again, 18 years later. Which version should I play?

[Toxy]

The DS version is the best.
It has the cutscenes that were introduced in the Playstation version, however with less loading time throughout the game.
It also has a new area therefore a new optional ending.
Improved dialog.

So yeah, get the DS version and play it on either the DSi XL or 3DS XL (and if you wait long enough the New 3DS XL).
That will offer the best experience due to the bigger screens.