High Elf Apprentice FTW.
You want robes and take all the mage skills (go pure) as long as you collect the right spells for your level and do mages guild you will be fine. Alchemy is BAWSE
Let me first admit i've not actually played a pure mage character yet, but i've played and read plenty to give some good tips.
Birthsigns:Wouldn't the Atronach be a better choice than the Apprentice? 100% weakness to magica sounds really dangerous especially if you run into a lot of casters (necromancers, conjurers, vampires, demora mages) early in the game before you've had a chance to build up an arsenal of protective spells and clothings. the spell absortion of the atronach is better than any defensive spell you'll come across early game and then late game you can easily create the spells and enchantments necessary to overcome stunted magica. If you're reinforced with restore magica scrolls and potions, you'll probably have a better time than if you were trying to wait on your magica to recharge itself on its own anyway.
Personally I find the more involved gmaelay to be more enjoyable and engaging, otherwise Oblivion is just a big hack 'n slash fest... or rather, cast 'n blast... in the case of mages. Anyay, if you're really against having to maintain your magica like that, you can go with the appretice and work towards the artifacts with http://www.uesp.net/wiki/Oblivion:Ring_of_Namira http://www.uesp.net/wiki/Oblivion:Saviour%27s_Hide http://www.uesp.net/wiki/Oblivion:Spell_Breaker as soon as possible. Add in the Spelldrinker and you should be good to go.
Then again, if you go with the Mage birthsign, you can skip on the negative effects of either of the above birthsigns, then you can follow the tips http://www.uesp.net/wiki/Oblivion:Magicka to still get your total magica up to a rediculously high level (900+)
Leveling:Ok, that's enough about birthsigns. as far as making a really powerful mage, other than just using a high elf, try following the http://www.uesp.net/wiki/Oblivion:Efficient_Leveling guidelines. Basically, you use some non-desirable skills as your major skills, ideally these would be ones that you rarely use but are easy to level/grind. For a combat char, it's easy to grind magic skills with lots of little "on self" spells, for a mage, you could choose some skills from a school you will rarely use and then add in some oddballs, and make use of the http://www.uesp.net/wiki/Oblivion:Increasing_Skills#General_Combat_Strategies if you need to grind a combat skill. When you play this character, you monitor your "primary" skills closely, i.e. the ones you actually use and want to get good at. you make sure to get as close as possible to having exactly ten level ups of your choice skills per attribute. For example: if you start with... i dunno, let's say 30's for your majors (the skills you rarely, if ever, use), and 15's across the rest of the board, and you want to get +5's on INT, END, and WIL, then you could get conjuration, alchemy, destruction, armorer, and block all up to 20 before grinding any of your major skills until you level up, assign the +5's and proceed back to regular gameplay. This really only requires intermittent monitoring as you play becuase the skills system are, for the most part, blaenced. You will probably hit those magic 10 skill increases at about the same time if you're using the skills you planned to. You don't even have to have exactly 10 skills increases under each attribute, and you can grind a bit to even them off if needed, then all you need to do is grind for like five or ten minutes to level up and you're good to go. You just continue this, aiming for particular attributes each time and planning ahead. Because you're getting the most out of each attribute increase, you're probably going to grow quite powerful even by level 2 or 3. Additionally, this will maximize your total levels gained. If you choose your major skills as throw away skills that get a mimimum of racial bonuses (easy with races like Altmer and Redguard that are geared at a single type of combat) then it should be fairly easy to get your character up to the true maximum level of 55 without using any exploits. Personally, I like to make a spreadsheep to keep track of my progress, but it would also wok if you want to juswrite down your starting and ending skill levels for the skills you want to focus on each time around... or even just try to remember them! as long as you stay pretty close to the magical 10 skill levl increases under your desired attribute each time, then you should be just fine. There are more than enough possible skill levels to cover and slop, you just might have to grind a bit late game on a lesser used skill to even out the numbers.
Gameplay:Make the most of alchemy and enchanting. Even if your mage is primarily a caster, weapons like shortswords, bows, and daggers can make for great vectors to deliver really monumentally destructive poisions or enchantments. Also it's worth taking a few minutes to look through the http://www.uesp.net/wiki/Oblivion:Quest_Timing suggestions. Most of these should be obvious to a seasoned player of Oblivion, but there are some good tips (don't worry, it's short and has minimal spoilers)