I liked those old games. I played through all four of them. I'm not a total FF freak, so if my history is slightly off, please everyone, hold off the rampant flaming.
The Final Fantasy Legend I, II, and III games were part of Square's SaGa games in Japan (some of which were released on PlayStation). These were turn-based RPG games that centered more on gameplay than story. You won't see a lot of similarities with other console FF games simply because they weren't really part of the series. If I remember correctly, Square attached the Final Fantasy moniker to the games to sell a familiar brand overseas.
Now Final Fantasy Adventure is a different monkey all together. This was Squares first adventure in the Seiken Densetsu series. Later these games became more commonly known as the Legend/Secret/Sword of Mana series. This is an action-based RPG, and is similar style gameplay to the original Zelda, or the Zelda series on GameBoy. This game was recently remade on the GBA as the Sword of Mana. New story and other updates were put in for its re-release.
All four games are worth playing. I played through FF Legend I, II and Adventure several times growing up. There is nothing totally unique about the series, but they are fun on long trips. If you do plan on purchasing Sword of Mana I would hold off buying FF Adventure since it's essentially the same game.