You don't need to play the previous ones - they're all separate stories.
If you want an in-depth walkthrough, gamefaqs should have plenty. (full social link guide, persona fusing guide, etc)
And as for tips... Well, fuse new personas as soon as you can. Once you reach lv 8, try fusing a Lilim - its multiple element attacks can come in pretty handy.
Also, don't overexert your characters - if more than one enters "tired" status, get out and save/rest.
In the first couple areas, get ready to be constantly killed. P3 isn't easy, and the party member AI isn't always the brightest (I'm loo