Start the game with 3 Minion Dematerializers. Killing minions with the item gives permanent bonus damage vs. that minion type.
+5 AD or 9 AP
+6 Armor or 8 MR (match-up)
Ryze's natural spell-spam nature allows you to easily proc Phase Rush with [W]->[E]->[Q] and stick to your target for follow-up damage.
Ryze naturally stacks mana with Tear and RoA so you gets extra mana returned allowing you to spam a lot more spell in the mid-game.
If you're playing into multiple magic damage threat, take Nullifying Orb.
Celerity's extra Movement Speed synergizes well with Ryze's [P] movement speed burst to help you position and kite in fights.
Gathering Storm is a great late-game insurance policy that scales incredibly well the longer the game goes on, allow you to deal insane damage at 40mins+.
Paired with Cosmic Insight, your mid-game skirmish potential will be incredibly strong having a great mix of AP, Health, Mana, and CDR. Cosmic Insight is also great on mid-laners who take Teleport for the shorter cooldown.
Minion Dematerializer empowers your ability to wave-clear effectively for roams and synergizes well with Ryze's [E].
If you Dematerialize a minion and cast [E] on it, you will get a guaranteed [E] spread.