This is going to be a fun thread to skim
I would like to point out that any story can be boiled down to: bad guy wants to do X, heroes stop him. Such simplifications can be applied to any game to defend ones preference and are of no use.

FFI
Time loop? Though not mind numbingly difficult it blew way over my head when I first played FFI, mostly because of how simple a story I had been experiencing up to that point. Most definately not simple.


FFIII
The story was fairly simple, but threw in a few plot points that deviated from the norm. The most difficult points to grasp would be why the gift of mortality would be considered the greatest gift of all, and that the World of Dark wasn't anymore evil than the world of Light, and the consequences of Light overwhelming Darkness were just as dire as Darkness overwhelming Light.


FFIV
FFIV's story was very involved and epic, but there wasn't anything difficult to conceptualize. I would say that the story was very easy to understand.


FFV
I haven't played it in a few years because I've been waiting for FFV DS, so I'm a little rusty on the fine details. Understanding Extedeath was a tree was something I knew a few people somehow missed, as well as the nature of the void. Other than that the story was fairly straightforward.


FFVI
Thinking about it, the strength of FFVI was characters not plot. The plot I believe was very good, but it is the characters who make the game. The story was very simple to understand, it was the more subtle character emotions that were harder to understand. The whole Celes cliff scene totally went over my head when I first played it, I though she was just upset and went to do some cliff jumping to blow off some steam.

Way to miss out on the most powerful scene of the game.
...
Don't laugh at me!


FFVII,VIII and IX
Come on, are you joking?

FFX
In FFX the goal was very clear the entire way and did not change. However, as it was noted earlier the whole Zanarkand/dream thing was a little bit to get your head around.


FFXII
I thought the whole plot to FFXII was brutally simple and easy to understand, but a lot of people seem to find it to be a little hard to follow. I attribute this to it being the first one that had a little more focu on politics. Imo, the politics involved in the game are certainly a step above average FF fare, (which isn't saying much), but still incredibly simple.


FFXIII
The plot of FFXIII was very simple, just hard to understand due to lack of explanation. A.k.a. it wasn't hard to understand because it was complicated, but poorly told.


And, after taking time to reflect on all titles, the winner is FFIV for not having anything that is out of the ordinary to understand.