Undertale is my top recommendation, unique turn based gameplay with great humor, soundtrack, and story. (It's a game best experienced and not spoiled)
Final Fantasy 9 is, in my own as well as Nobuo Uematsu's (The composer for the music of the FF series up until XI) favorite Final Fantasy. 7 is famous for being one of the games that made RPG's popular in America, so that one's good as-well... Though I hold the unpopular opinion that 9 is better.
The .Hack//G.U. series is a story heavy, 3 part RPG that's a bit more action based, but quite slow to get going... in addition, the anime series is meant to be watched alongside it, so it's quite the investment if you want to look into it. It's known for it's use of Red Herring, mystery, drama, and symbolism.
The "Tales of" series is considered many to be quite good... personally, I've only been invested in Tales of Symphonia... possibly the most famous of them all.
Star Ocean: Second Story or any of it's remakes is, without a doubt, the best in a series of mediocrity... The first in the series being good, this one being fantastic, and everything after better off as expensive pizza cutters... To this day holds the record for alternate endings (Approximately 80, 100 if you get the Second Evolution remake) combat is a unique take on action based, and the voice acting can make your ears bleed if you get the PS1 classic. I think they swapped it out for the remake...
Grandia 1 or 2... Both great games, but the fanbase is quite split... sports an interesting turn based combat where you can actually flat out stop an enemy from executing an action based on timing.
The Disgaea series isn't particulalry well known for it's story, but it's very well known for it's humor and over-the-top strategy RPG style... lvl 9999, 1,000,000,000 dmg, counter-counter-counter-counter-counter-counter-counter-counter-counter-counters? All possible in this crazy series.
Dark Cloud is steering away from the turn-based aspect, but it's a great 2-game series none-the-less with the ability to build towns, go fishing, and more... especially if you get Dark Cloud 2 where you'll be hard pressed to run out of things to do.
And lastly, Final Fantasy Tactics... ig you want a Strategy RPG like Disgaea, but prefer story over crazy, this is a great choice... though the AI is rather relentless, so be prepared to re-load those saves... MAKE SURE YOU USE MULTIPLE SAVES.