The problem with Ryze is that until now he has a very gerneric and not really interesting mage-play pattern. Walk close-> throw all point and click stuff -> repeat until target dead.
Another point would be the question on how to handle the mana issue here. I think in it's current form the mana-scalings have to go.
About his new skills... well, that's kinda hard to say since this is actually designing an entire new champ with a very few guidelines you can follow thematically (just like Sion back then). For that we need to get down to the question of what we actually want Ryze to be? A close combat mage? A mid-range burster? Some kind of AP Bruiser? Or maybe more of a pure mage more focussed on dps than on burst?
What do we actually WANT him to do in the teamfights? Is there a special niche he could fill?
My idea would be to keep him somehow connected with "Mana", but not in the way it currently is. A passive granting him bonus mana the more AP he builds seems to be a good start here.
The problem is: this would, especially in combination with
, grant him A LOT of ressource. But how do we get someone with so many ressources to actually have to manage it? The solution os quite simple: his spells get %-Max and %-Current mana costs. (the second option for weaker spells of course).
For his ultimate I propose a channel that burns almost all his mana, but deals more damage the more mana got burned. I mean, it's called "Desperate Power" if I remember correctly. Blasting all you have in one spell seems quite desperate to me.
About the actual basic skills... hmmm I think there should be another interesting mechanic to add here. Mana-Drain (sounds like an interesting concept if he's supposed to be all about Mana), bouncing projectiles (but not automatically bouncing like his W is currently, but you can aim it at walls or minions and try to hit the enemy with that), his runecage could be a dodgeable AoE similiar to Brand's W, etc etc.
I think if Riot's designers get to work they will come up with much more interesting stuff than I wrote her right now ^^