You don't mind 2D PS-era graphics, do you? You aren't really going to get Crysis-level stuff from JRPGs anyway, so I assume you don't.
Final Fantasy titles are good, but I'd dare say they are more about style and flair than cohesion. All JRPGs feature tight linear storylines, so limiting yourself to the FF series is unwise. More than the stories, they feature this specific flavor of JRPG, always with the same character archetypes, same themes, plotlines, tunes, references to older games, etc. If you're not a FF fan, you'll likely ignore what most FF fans buy the games for.
If you want superb storytelling, I'd recommend starting with FF9. It's cute, colorful, imaginative, epic, has interesting characters and a rather simple, but nicely-told story. The classic JRPG pitfalls are almost completely absent, the fights are quick and pretty, the mechanics are really simple and efficient, and most importantly, the game as a whole is endearing and memorable.
In comparison, FF8 has a convoluted plot, unlikable characters, complete lack of focus and central story, bad dialogue, horribly unintuitive and abstract game mechanics, and overall feels like a committee-designed FF7-extract.
FF7 probably has the most thought-out story of the series, and a must-play simply for its classic status, but I felt FF9 had a bit more soul to it. The setting and feel is very well designed, but the graphics may be a bit dated. Early-3D doesn't hold up that well.
FF10 is basically FF13 done right, though I still dislike the complete lack of freedom. The plot of 10 is also rather convoluted and badly-written, but it doesn't feel that way while you're playing - the entire game has this "road trip"-vibe, never deviating from the central story, and seemingly very focused (even if it doesn't hold up to critical analysis). The world and character design are, frankly, unappealing, but that may be my personal gripe. The personalities and relationships of the characters are above average, though.
FF12 is so damn perfect as far as game mechanics are concerned that playing is almost effortless. If you set up your gambits properly, you can play the game with just the left stick for movement. As much as this is an admirable achievement, do you really want to play a game without actually playing? Besides, it's barely a FF game - it's made by the FF Tactics team, set in the same universe as Vagrant Story, and generally diverges from other FF games in theme and feel, concentrating more on international politics than any save-the-world quest. It's by no means bad, it's just rather bland and it feels off.
I sincerely recommend trying the Suikoden series instead. It features much more involving stories, it never feels ostentatious or forcibly spectacular, and it takes place in a cohesive and interesting world. The games mostly focus on the political machinations between countries, raising liberation armies, defending against tyranny, and so on, but the stories are all very human and very touching. Suikoden 2 is generally regarded as the best in the series.
Also, pretty much any JRPG by Atlus, their Shin Megami Tensei, Digital Devil Saga and Persona series are all excellent. I haven't seen much of them, but I've heard great things about their quality.
Another favorite of mine is the aforementioned Vagrant Story, another brilliant PS1 title by Squaresoft. It's very unconventional, and concentrates more on atmosphere and dungeon-crawling/puzzle-solving than linear storytelling, but it's original and unusual even today. The story is a kind of Renaissance occult mystery thing, and sadly it was never continued in a sequel. Definitely a refreshing title.
There is also the Tales series, of which I have played only 3 games, but I'll recommend Tales of the Abyss because it has one of the most amazing character arc for the protagonist that I've ever seen. The series is typically famous for its self-aware humor and great characters, and I thought Abyss had the best of those.
R Not a bad game as such but there are better places to start.
