Bruiser Ryze
So this is definitely not the best build ever, I'm sure it could be better, even for the role of a bruiser. However, I think these items have an interesting interaction with each other and Ryze.
Build
Items
No, this isn't meant to be an AD Ryze, the mana is of course great on him, and the Shock effect works well because he has a lot of single target abilities.
The health adds to his ability to survive, the mana of course helps with his ability to deal sustained damage. What I love most about this item is that the Eternity passive is amazing with Muramana. Despite having just tested this in a bot game with the intention of testing this specifically, I didn't actually pay enough attention to see it. I'm pretty sure the Shock empowered auto attacks and single target abilities will consume 3% of your current mana, and Eternity will then heal you for 20% of that total. (I also want to point out that the passive does say it will heal for 'up to 25 per spell cast' but again, I am not sure how this applies). Also, because of Eternity the damage you take will be converted into more mana, which will give you a greater amount of current mana, to buff Shock.
For a more offensive option 
would of course give the same amount of health, more mana, and 100 AP, which means more damage and more mana, but being more expensive and taking longer to stack can be a problem.
Simplest reason for this item is that it provides the most mana of any item that doesn't require stacking. It also helps with his resistances with the armor. The Spellblade effect on this wont be as useful since auto attacks will mostly be an accident, but it definitely wont hurt you when it happens.
Probably any boots would be good on him actually. Of the items I have in this build, he would be at 30% CDR so this would bring him up to 40%. More movement speed will always be good, so Swiftys or Mobys would still be good. He does deal magic damage so Sorcs could help. As a bruiser, resistances are good, so Ninja Tabi or Mercs would be good too. You could even make a point that having a decent amount of AD and the Shock effect would make Beserkers a viable pick.
I really felt this build needed MR. The 10% CDR. base health, health regen, and the increased healing is great for his sustain. I would have really liked to grab another mana item, but I think this fits pretty well.
Lastly, top him off with the hat. Honestly, there may be a more efficient item here because he wont really have much AP otherwise at this point. Basically, getting lots of AP here at the end will not only increase his AP scaling on his abilities, but it will further increase the amount of mana he has accumulated up to this point.
Runes These are the runes I plan on using.
Marks: Hybrid Penetration Seals: Mana per Level Glyphs: Ability Power per Level Quintesences: Currently I have Ability Power per Level, but once I get Mana per Level, I am thinking that will work better.
As for Masteries, I am having trouble deciding which is better for his keystone, Deathfire Touch or Thunderlord's Decree.