Chrono Trigger is one of the top RPG of the 16 bit era (for me only beaten by Terranigma) so keep your expectation in check.
As for the RPG in the SNES Classic, they are quite different so it's quite easy to make a choice (on what to play first) depending on your tastes.
Super Mario RPG: RPG that targets newbies of the genre therefore there are action sequences both in the form of mini games and timing commands to increase damage inflicted or the parry effectiveness.
It has turn based battles with some action and visible enemies on screen.
Oh it is also notable for to be one of the few SNES games to use full computer generated graphics.
EarthBound: The best description would be "a weird combination of Dragon Quest template and Peanuts".
It has lots of charm and it's the most mature RPG (in the sense that target adult thinking) of the era despite having children as protagonists.
Turn based battles and visible enemies on screen.
Final Fantasy III (VI): It's the best Final Fantasy.
Turn based battle (although the priority of the turns is in real time) and random encounters.
Secret of Mana: It's the only action RPG on the list though don't mistake it for a pure action adventure like Zelda because the battle system is a mix between Final Fantasy battle system and real time movements that is battles are still ruled by statistics (you can't dodge spells for instance).
It's notable for to be one of the rare case of co-op RPG of the era so if you have a pal to share your enjoyment of the SNES give it a go with him/her.
Thank you for this awesome write up! I'm starting Mario RPG due to my background with that series, but I'm excited as hell to play FF6 after that since I have never finished a classic FF before. This will be a first!