Alright, here's the breakdown of stats and what-not.

On the US version of FFX (a.k.a. Beginners Grid on European version), there's a total of 828 sphere nodes on the grid, 77 of which are filled with abilities (Info. gained from GameFAQs' FFX Sphere Grid FAQ), leaving you a total of 751 nodes for stats. It's impossible for you to max out ALL stats, but you can max out most of the stats, basically everything except HP and MP. To max a non-HP/MP stat, you'll need 64 spheres of +4 of that particular type. There are 8 non-HP/MP stats, so if you want to max them out, you'll need 512 of those 751 nodes for that, leaving you with 239 nodes for HP and MP to split as you see fit.

And yes, you're going to need Clear Spheres. A LOT of them.