Wow, so many here started on the PS1.
My experience started when I was looking for Zelda-type games on the SNES. Came across quite a few decent ones, only two stand out to me at the moment: Illusion of Gaia and Secret of Mana. After playing Secret of Mana, I followed Square to see if their other games were just as good. My first Final Fantasy was III (VI) on the SNES, and my initial reaction was that I hated it (first menu based game I played). After some time, I tried Mystic Quest and enjoyed it, then moved on to IV and loved it, and finally decided to give VI another chance, and I loved it, too.
Not many in Australia knew about Final Fantasy back then (I'm thinking around 1994 or so) since the only copies that could be played here were imported copies with a converter, and Final Fantasy VI wasn't quite PAL compatible even at that (the menu screen occasionally blacked out inside towns, and the ending for the game would crash out halfway because the picture couldn't keep up with the music).