Just so there's some love, Final Fantasy 8 is my favorite Final Fantasy game, and I find 13-2 to be a pretty decent game over all and a vast improvement over 13. That being said, 13-2 really not a great game to measure the series with, as it is rather different, same with 13. 10's more in line with the others, just lacking over world exploration and lacking being able to fly a damn airship.
OP, it sounds like you may enjoy 12, but I'm not positive.
Personally I think the core Final Fantasy experience can be found with the SNES and Playstation titles. 4, 5, 6, 7, 8, 9, and Tactics. I think choosing two or three from those gives the best idea of what Final Fantasy has been. From the dawn of the ATB gauge, refinement of the Job system, The era of customizable character stats, from 2D to 3D, to 7 bringing cut scenes into the series.
I'd say story wise, I think 9 starts out with the strongest story, not to say it drops it, just I think those first few hours are a good measure whether you'd like the rest of it. 4's is a pretty solid classic redemption story. I think 5 is a little on the weaker side, story wise - gameplay wise it may be the best job class system in the series.
Then there's 8, I wouldn't recommend 8 for it's story, without strong cautions(which that word doesn't have an "S" in the middle of it, why did I just spend two minutes trying to type cautions with an "S" in the middle?). Final Fantasy 8, from the opinion of some who adores the game, is, at times odd, crazy, senseless, and "WHAT?!" inducing. Ignoring gameplay for a moment and looking at the story, some spoilers, spoilers -> with paraphrasing .
Squall - Missiles are coming for the school!
Everyone Else - Do Something Squall!
Squall - Like What? Why Me?
Everyone Else - I don't know, something, you're in charge!
Squall - I don't wanna be in charge! I just graduated last week, why the hell am I in charge?
Everyone Else - The school used to be a shelter or something, go to the basement!
Squall - Fine!
Squall goes to the basement, pushes a button, the entire school lifts off from the ground, flies into the air, and moves out of the way of the incoming missiles. Smooth landing into the sea, and drifts the ocean blue. And I love it.
Brief micro special things that happen that fill me with joy
There is a Dance Scene, a dance scene that may be summed as a Dance Off
Zell, a hyper active who wants to touch your sword, because your sword is cool, because your sword is also a gun
Also, the hotdogs. The hotdogs at school are awesome, but they always run out
Delusions of White Knight hood, fighting off evil villains
Orphans!
Dog Cannon, a dog that fires off your arm like a cannon, also, gives you wings
Squall's teacher comes onto him
Squall's teacher has groupies, and all they do is gush about her
Seifer has groupies, and all they do is follow him around, direct, no excuses, no BS, they follow him, cause it's what they do
We're going to die, I was put on this team to die because Squall doesn't like me
Wah! We're in prison! Don't worry in my dreams, where I see the past, I was a janitor here, I can lead us out!
The End of Disc 1 is fun cut scene