No, you don't need to play 1 and 2. In fact, it's better that you start with 3, since it's the one that introduces the social link feature. P1 frankly blows, while the two P2 titles are great, but not entirely friendly to newcomers. Best check out the later titles first, then come back if you liked them.

This is one of my personal faves and you should read my entry in it in my top 25 list as well If you're playing for, go for any version that isn't the original release, since they streamline a lot. While FES is cool with it's additional features, I found the additional scenario weak. P3 Portable gives you two protagonists to choose from (the female path is awesome), you can control all party members in battle, and in general it's just much more user-friendly. But you get a kind of simplified interface because of that - it's all much more visual novely, but you can get used to it.

And be prepared to face the most tedious dungeon ever. But the writing and amazing characters more than make up for it. It's a gem that needs to be played by EVERYONE.