I'd recommend finishing Chrono Trigger at the very least. Just make sure to properly save this time around.
If you want some other decent starting places, consider Final Fantasy VI (IV, V, and VII are also rather well liked), Dragon Quest (III, IV, and V tend to be fan favorites), Paper Mario (both the N64 and Gamecube ones; also Super Mario RPG for the SNES, though it’s not quite the same), and Mario and Luigi (especially Superstar Saga on the GBA) for Turn-based/ATB systems, and Tales of Eternia/Symphonia/Vesperia (playing through most of the localized games in the series, those have struck me as good starting points) and some of the Mana games (Final Fantasy Adventure/Seiken Densetsu, Legend of Mana, Seiken Densetsu 3, and Legend of Mana are generally well liked) if you want real time combat. Also plenty of other series (Baten Kaitos, Breath of Fire, Grandia, Legend of Heroes, Lost Kingdoms, Lufia, Lunar, Mother, Phantasy Star, SaGa, Shadow Hearts, Shin Megami Tensei, Star Ocean, Suikoden, Valkyrie Profile, Wild Arms, etc), as well as standalone games (Infinite Space, Lagrange Point, Radiant Historia, Rogue Galaxy, Skies of Arcadia, Vagrant Story, Xenoblade, Xenogears, etc) if you find yourself liking them.
Big thing to keep in mind is that there's a lot to pick from (even more if you're willing to look beyond the mainstream for more niche franchises like Atelier and Ar Tonelico, or go for fan translated ones as well, as they're popular to patch into English, even if it takes a long time to translate), and even if one particular series or gameplay style doesn't do it for you, try another one rather than writing them all off. Also plenty of fan translated ones that never came west.
That’s also not taking into account the swath of tactical JRPGs as well: Dept. Heaven, Disgaea (as well as various other NIS tactical games like Makai Kingdom, Phantom Brave, and Soul Nomad), Final Fantasy Tactics, Fire Emblem, Front Mission, Langrisser & Growlanser, Ogre Battle & Tactics Ogre, Shining Force, Super Robot Wars to name some.
Yes this is partially copypasta, I have this saved since I didn't feel like typing this up each and every time the question comes up.