STARTING ITEMS:
OR

Take boots if you feel that the early movement is neccesary.

BOOTS:
OR

If the enemie team have high CC And/Or high magic damage, tenacity is a "must have" since ryze is most of the time standing in the middle of the fight because of his short range.

CORE ITEMS:
AND

Build Tear Of The Goddess before you start building Cataclyst The Protector, this gives you some extra time to stack up some early mana for the lategame Archangel Staff, If ur being bullied around in lanephase its a good idea to build Cataclyst The Protector, the Health and the Mana is going to let you be more offensive and the Unique Passive is giving you a nice sustaing during lanephase.

This is how i recomend that you build after the items above:

First you will buildNext thing to do is to upgradeTOORDepending on what you need. Then finnishNow its time to upgradeTOIts time to finnish of the build with 2 of these items

This build allows me to Deal damage compared to any other AP/Spellcaster, And the Armor, Healt and Magic Resist lets me stay tanky enough to stay alive most of the fights. The combination of Durablility, Damage And AoE (Ultimate) Gives Ryze the Ability to not only burst down single squishy targets, but to take on larger fights alone, for example against a tanky fighter or to face a carry with support alone.

Try to make your own build, try to play with all of the items above to find your own build.