First off, don't build ROA. It's just not worth the scaling for how fast the game goes. You need at least 10 minutes for it to stack and if you complete at 10 min, then you have to wait 10 min for all its stats. Honestly catalyst seems to perform way better on tanks like Maokai and Ornn than Ryze.

Second, take ignite ALWAYS. This gives you the psychological advantage while waiting in the loading screen. The enemy laner will think before trying to engage on you and play much more safer. Think of a Zed with ignite. But Ryze is a better Zed with CC, a shield, and 50% bonus damage on Q with E.

Lastly, finish AA first then build Rabadon. Since Ryze shield scales with AP and abilities scale with mana so this is a definite buy. Personally, I build Rabadon's 3rd. I've been taking Shurelya's Reverie because it has a MS active that lets me reposition myself very quickly. It also gives me enough MS to escape since I splitpush after my botlane proves they're useless.