I'm playing my first ever atronach at the moment, but it's not a pure mage. He's a battlemage, and I find him really easy to play. One reason is that I play a breton, with 50% resistance to magic.
Against magicians, I have nothing to fear. 50% absorption usually gives me more mana than it costs to heal from the spells that DO land. In fact, it's a great way to get an almost empty magicka bar filled. Against melee, I have to make sure I kill them quickly enough to not run out of mana. Since I wear weapons and heavy armor, it's a lot easier than for a pure mage. But for either, the key is having good shield spells, and tons of restore health and magicka potions. Do note that other potions, if applied correctly, can help you a great deal as well. The key point is that you need to focus on your alchemy to help you with stunted magicka, and you need to minimize the amount of damage you receive. Good enchants would therefore be shield enchants, and of course fortify magicka. Spell absorption will make you even more powerful against magicians, until the point where they can't hit you anymore.
When you are in a city, always go to the chapel to restore your attributes (if you have higher fame than infamy). Carry restore magicka potions wherever you go, and anything else that's useful. Consider using weapons to save on mana (a pure mage could still use enchanted staves without RP problems), or rely on chameleon and command spells to avoid fighting entirely. Make sure you keep spellcasters alive till the end in a mixed fight, and let them hit you as much as possible to get your mana refilled freely. Try to avoid fighting a number of melee enemies without spellcasters, because you will have to use potions. Combine damaging attacks with weakness to ... to make your spells more efficient, and anything else that minimizes magicka use.
Also note that while the atronach can be hard during the initial levels, he will get stronger later on, when enchantments make up for your vulnerabilities.