After checking the Wikipedia article, I did discover that none of them are really linked in any significant way. I guess I want to play them all just for the sake of doing so. I guess I'm kind of silly for it.
You are, but we won't hold it against you. I myself went through the same phase as a teenager. I wanted to play through the entire series just for the sake of it. I learned my lesson on my own that it really wasn't worth the effort. You will too.
Anyways, if you're going to commit heavy undertaking of grinding through the series, I'd recommend doing it in the following order (Give or take through the middle, but this is my recommendation):
1, 2, 3, 8, 4, 9, 10, 5, 6, Tactics, 12. I glossed over 7 because I get the impression you've played it already. If not, I'd say play it between 10 and 5. My reasoning is as follows:
If you can grind through the first two, you should be able to hoof your way through the series. They're easily the shortest entries, but they legitimately felt like a chore to me by the time I got to them (My original playthrough order was 8, 5, 6, Tactics, 7, 9, 4, 10, 1, 2, 12, 3), especially two as the 'leveling' system is an absolute load of shit. The story in both is also rather lacking as the original is essentially just on long, scripted fetch quest. Three's story was pretty bland as well and the battle/job system is, as I mentioned, basically a stripped down and inferior analogue to the one in five. Eight...well, it looks pretty and the story has the occasional bright spot, but it eventually gets incredibly convoluted and the magic and stat system is pretty garbage. Four is touted as one of the best stories in the series, though I never really got into it. There also aren't enough original battle elements to warrant it as anything special. Nine had a pretty generic battle system and story as well and I'd honestly say it's interchangeable with four in many ways, though it's at least prettier, I suppose. Ten had some very nice new battle elements and most people (Myself precluded) loved the story. It's a bit of a quality jump from the first six entries I mentioned, so it's probably best played after them. Five had, until recently, the most absolutely unique and inspired character stat system with the job system. It's a grind-fest, but the flexibility and customization of the system makes it a blast to level. Six is my absolute favorite and had, bar none, the best story of the series (Many people like seven, but I find the story needlessly cliche and convoluted). The battle system is a tad on the generic side, but the mix or music, story and overall presentation make it a must play, you'll also appreciate it that much more after playing the other, more inferior games, earlier on. I put Tactics after six because it's best played in conjunction with twelve. I personally hate turn based strategy games of the like, but it was one of the best FF stories and is commendable for that alone. If you're a fan of the TB strategy genre, you'll likely love it (It's also just been ported to PSP). Twelve is last because it's easily the best looking and biggest departure from the series. The story is rather bland, but it's the absolute only FF game I never got bored playing. The combat system is an absolute blast, especially if you enjoy the occasional MMO. I found myself legitimately enjoying grinding trying to fill out the license board.