Basically the Expert grid has much less level 1 and level 2 key spheres, which gives you a lot more freedom.

You should stick to what the game says and choose the standard grid if it is your first game, because you may get confused and take Lulu down Auron's path accidentally, which makes Lulu obsolete. But the other way, if you know what your doing you can move do something like take Tidus down the beginning of Rikku's path and get a major boost to HP, or take Tidus/Wakka through Auron's for a while where you gain A LOT of strength and HP at the cost of Agility (Tidus) and Accuracy (Wakka). Or drop Lulu into Yuna's to get Cura or vis-versa.

I think one of the grids is slightly larger as well, I'm not 100% sure which one.

No matter which grid you choose, the characters will have their starting abilities. Yuna will have Cure/Nuls (Esuna? Can't remember), Rikku will have Steal/Use, Kimarhi will have Lancet etc.etc.