http://www.gamefaqs.com/console/psx/game/197341.html

Scroll down to 'In-Depth FAQs' and then click 'Plot Analysis'.

This gives you an entire analysis of FFVII's plot, which should more than prepare you for Advent Children's storyline.

And yes, each and every Final Fantasy is set in a different world with a different storyline and different characters, with the exception of Final Fantasy X-2, which is a direct sequel to Final Fantasy X.

As for which storyline is the best, that's all just a matter of opinion really. On a personal level I think Final Fantasy IX had the best plot.