My Ryze build is pretty simple, start going for mana and either armor or magic resist depending on situation.

Items for Ryze are pretty obvious, lots of mana and survive. With this build items are obvious up to the Glacial Shroud you can rush Banshee's Veil instead depending on situation. And sometimes i will get two Frozen Heart instead of a Banshee's Veil and vice versa depending on other team full of tank/melee - mage/range or not. Also might throw an Abyssal Scepter on instead of Lich Bane depending. Lich Bane is just a nice finish i think. I like Ryze passive zap attacks, they fit in the overload/rune prison rotation well :)