the only reason I tend to get mana shard first is the extra mana in the beginning can keep you in your lane longer if your a harasser (like me) and will boost your damage output just because of ryze's abilities. Also since I was trying to make a mana focused build I just like it more. But I can defiantly see getting ring first then going for tear.

well, if you're calling it a build, here's my recommendation itemwise, since i see that you don't have then figured out as you said. i would start with a Doran's Ring, go to sorcer's shoes, get a Archangel's Staff, Rod of Ages, a Banshee's Veil, Frozen Heart, and end with a Rabadon's Deathcap. this set-up gives you tons of mana and ap, with nice synergy between them.

i would also remove 2 points from Deadliness to put 1 each in Sorcery and Archaic Knowledge . fyi. any questions, pm me.
gj, gl, and +1