OK so if you haven't played any of the preceding FF games, and you jump in to buy FF XIII, will you be confused as hell or does the storyline in each game "start over" ?

its a new world new story ect for each ff. Each final fantasy usually deals with some apocalyptic character or being about to destroy or take over the world with some other minor undertones. If you played JRPGS wont be a big transition for you.

no, youll understand it but ff veterans probably know more strategy since theyre so familiar with the commands and stuff

some people say this will have the greatest graphs in the world till now

I'd reccommend you to start with VII or X
But do as you please
And have fun with FF-serie