Straight Ryze build, simultaniously building mana and AP for the most damage on all three basic abilities, building durability aswell. Ryze is my favourite caster in the game, this is the way I build and play him, and and get horribly fed in normal games pretty often, so i recommend you giving it a try.

I pretty much roll tank runes on Ryze, because starting with a Sapphire Crystal is pretty much the same as not buying a starting item. Though it gives you some damage for Overload and Rune prison, and a greater mana pool, you will miss that 100 health from Doran's Ring, because ryze is squishy even compared to other casters.

Basic caster mastery: Magic penetration in offence, and all the utility you can get.

Some start out with a meki pendant, wich is a pretty bad descision in my opinion, becuase it doesnt give you that early chunk of damage from your max mana, and you cant really use that regeneration for any good, as you want to throw as many Overloads at the beginning as possible. You will likely get plenty of mana from leveling up, if you go mid, and honestly you want to go mid, as ryze as a duelist, and doesn't have any escape mechanisms except for your summoner spells.
I always start with Sapphire Crytal and 2 Health Potions, its just great to have that extra 400 health.

You might say, that getting Tear of the Goddess before Catalyst is better to start stacking mana early on, you really want that sustain from Catalyst's passive, and the Durability you miss not having a doran's ring.
By getting Rod of Ages and Archangel's staff right away, you can start to stack them fairly early, thus gaining the most AP, HP, and Mana the cheapest way.

Banshee's veil is to furher increase your durability versus mages and initiations on you. Melee champions, or even AD carries shouldnt be a problem, as they can be stopped by a rune prison or nuked down right away if squishy.

Will of the Ancients is a very important item, really crucial to your survival in teamfights and smaller skirmishes. In team fights, with this, and Desperate Power, you will have 50% Spell Vamp, wich pretty much heals you for quite a big amount of damage dealt, disabling them from focusing you easily.

Frozen Heart is against endgame hard carries, and for almost maxing your cooldown reduction.

You might want to sell your Sorcerer's boots for a Mercury treads if it becomes a close game, as it is much more useful in teamfights, plus in those games that 20 magic penetration really doesnt add much.

You start up with Q. Not rune prison, because you really dont hurt your enemy much just by stopping them, and you cant spam that ability. Spell Flux is not really the thing you want, thought as a single spell it does the most damage overall, you can hardly use it to its fullest potential. You want to constantly Overload your opponent in mid, every time it's off cooldown. you are much more spammy with Ryze, than most mages, and if want to pick a fight, you can easily outdamage most champions earlygame, and it also outranges most caster spells.
If they let you harass them enough, just flash in, R+Q+Ignite+Q=First Blood. They cant escape that way, and thats why you want to take ignite even if its not that useful for ryze mid-endgame.

You want to max Q and W simultaneously, as these two spells will be your main and only damage until you get AP from RoA and AaS. After you get those, E will be a powerful spell aswell, combined with R.

QWERQ is your main rotation, after that you try to throw even more Qs. Remember, your R will grant even your flying spells it's benefits, so Q and E in this basic rotation Will apply AoE and spell vamp. There are cases when you can barely catch an enemy with W. Don't miss the opportunity by stopping for a Q, you can mess up your rotation if you need to, your team will help with the damage you miss with the messed-up rotation.

Earlygame you might want to get the blue buff if your jungler doesn't need it, after that you don't really need it.

You kill creeps with autoattacks earlygame, and start last hitting with Q after Tear of the Goddess to stack it, then wipe out minion wawes with an REQWQ rotations, going to the top of the minion kill charts.

Always be careful, as you have no escape mechanisms except for flash. If you initiate, you can quickly burst down a carry, but if you don't have your back covered after that, you are in trouble. If you are on the run care to help yourself or your team with a W to escape.

With Ryze you can beat most casters and carries in mid, don't listen to those who say "Ryze is **** no one plays him". He has an awesome nuke, great range, no skillshots, thus reliable and fairly long root with Rune Prison, low cooldowns, and great durability if farmed well.

There are some champions you don't want to be up against as Ryze in mid though. Malzahar can hardly be beaten, becuase many players just ignore you with Mal and push your tower, wich you cannot prevent, due to his distance from you(he hardly has to be around the minions to kill them with the dot and silence. Caitlyn: same story, you cant harass her, so she pushes your turret down if you dont have a jungler who kills her a few times. Leblanc: You can easily kill a leblanc as Ryze... that is until she hits 6 and kills you. Cassiopeia: You Can beat her, but you must have ninja skills to perfectly dodge her spells and predict when she uses her ultimate, otherwise you get murdered horribly. Lux: Not as bad as Cassiopeia, but pretty hard.

Some of the easily beatable mids: Karthus, Vladimir(extremely easy), Annie, Veigar, Brand, Ryze(if you follow my build and he doesn't of course haha), and most AD carries.