Honestly, I tend to gravitate toward the earlier games of the series, specifically the first 5 games.
(Note: This is based off the original versions of these games.)
FF1: The start of the series, and interesting because you create your party (though that's limited to just choosing a class and a name for each character). While there are some issues (you can only learn a limited number of spells of each level, and some of the spells outright don't work, for example), the game actually can hold its own when compared to the next few games in the series.
FF2: I could call this game "SaGa 0", as one could see the SaGa series to have spun off from this game. One one hand, it's the first attempt at a real story (involving a rebellion against an evil empire; the game even *starts* with a battle that you're meant to lose (and I believe winning is impossible without cheats, even with tool assistance)); on the other hand, it's also an interesting experiment with RPG mechanics. Thing is, there are no experience levels; rather, your stats increase based on your actions, and your weapon and magic skills level up through use. The game does have its issues (heavy armor is a trap option, and there's still some non-working spells), but it is a game I do often enjoy (though I think just about any SaGa game is better).
FF3: Take FF1, but replace the term "class" with "job", allow job changing at any point (outside of battle), and increase the number drastically. This game gives the player more variety in party selection than FF1, with many new interesting abilities to play with. There's also some things you'll encounter early that normally come later in the game (you get an airship within the first half hour, though it can't go over mountains, for example). The problem, however, is that they failed to do the same to the enemies; FF1 and FF2 have varied encounters, while in FF3 often every encounter in any given dungeon feels the same. There's also the problem of the final dungeon being long with a point of no return and no save points.
FF4: Here is the first FF game that really focused on a story. It's also the first appearance of Active Time Battle (no longer turn-based), and interestingly enough the only game in the series (not counting the MMOs) where you can have 5 characters in the party at once. Unlike previous entries, there's no party or character customization; characters come and go as the story progresses, and their classes are fixed.
FF5: Take FF3, add a few FF4 elements (ATB and some cutscenes), and fix the issues I mentioned with FF3 above. Now, add the ability to gain ability points (ABP) in your current job, learning the abilities of that job; then when you change jobs, you can borrow any one ability that you've learned from a previous job. Basically, this is an early implementation of sub-jobs, which would re-appear much later (though only in the MMOs and some spin-offs, not the main series sadly). There's also one spoilerific event that the game handles much better than a comparable event in FF7. I really wish the FF series had built on FF5 rather than just throwing out the job system entirely in later entries. This is my favorite game in the series.
Zimerius: to be honest, i find most jrpg's, open world games and popular grand strategy games these days pretty limited in their presentation, it seems that the grand lady of the j's may have been a forecast of that what would come.
thank god for the action games, per genre, that have a fit story line and appropriately aligned situations...
hell, even a couple of hours of gears 4 beats almost every mentioned genre in terms of sheer fun ;-)
You might like Final Fantasy 4.
Also, the FF games, with the exception of FF2, tend to be rather constrained in where you can go, possibly (but not necessarily) opening up later. Even in FF2, where you can go almost anywhere right away, you can't actually do the dungeons out of order (except for the tropical island cave, and one dungeon whose first floor (only) can be explored really early if you're strong enough).
