Magic regeneration is not that important, the larger your pool of magic the faster it'll regenerate. So what you want is more Magicka over regenerate.
Conjuration will be your back up, allowing you to summon Dremora Lords, elemental daedra. With the added Dawnguard, you'll gain summons from Soul Cairn which benefit from the Necromancy perks. The Wrathman with full Necromancy perks will be able to take quite a few hits distracting your enemy while you attack from range. The Aetherial Crown + the Ritual Stone will allow you to raise up a large army of undead, being able to use the stone's power as many times as you want, the more foes you kill, the more your forces grow.
Illusion, with the right perks will just about work on everything except Dragons. Duel casting expert level spells is a good way to make sure it'll affect your enemies, causing them to kill each other, be calm and allow you to walk by or flee in terror from you. With Master of the Mind perk, you will be able to use Courage, Rally & Call to Arms on your undead if you are using the Crown, using all three will stack, adding in being a Vampire and Necromage perk from restoration. Your army will cut down everything, with increased health, they will not flee and they gain benefits in Archery, One handed, Two handed etc for ten minutes.
Alteration is your armor and also a good money maker, turning iron ore into gold ore will allow you to forge many rings and necklaces to gain a large profit for a very low cost. While also increasing Smithing, Alteration & Enchanting if you choose to enchant those rings. Mage armor perks are a must to survive, with the Lord Stone you'll gain an extra fifty armor rating and magic resist, that is another useful perk to take, also being a Breton stacks onto it. Paralyze is very handy also, allowing you to take down those who pose the largest threat while you and your summons/follower handle the others.
Restoration is always needed, it'll allow you to heal yourself & your followers and undead if you have Dawnguard. Lesser wards will block all dragon breath attacks, even from Legendary dragons. Used with the duel impact to stagger foes, taking on dragons will be much easier as long as you keep them at a distance, if it lands you fall back. They can kill you in one bite. Restoration also has some good spells against the undead, which you will face quite a bit in Skyrim, the circle of protection will allow you to recover while any undead who cross into it will flee. Bane of the undead is also a pretty cool spell. Though master level spells take too long to use.
Destruction is always useful, though not always needed. The duel impact will stagger foes when you duel cast your elemental spells, this will allow you to keep hammering a foe and constantly staggering them while your summons/follower take them out. Though don't pass up a good Staff when you get the chance, keeping your magicka bar up is what keeps you alive, the staff won't cost any magicka to use. A Mage with no Magicka is a dead Mage.
Enchanting is well rather self explained, it's needed. Allowing you to create good enchantments for cost reduction or increase your magicka pool. They also offer resistance to the elements and magical attacks.
Alchemy, while not classed in the same as a Wizard anymore, potions will save your life. They can offer what you lack on enchanting, fortifying schools of magic, to resistance and refill health and magika.
Luckily Skyrim doesn't have any Witch Hunters, so you should be rather fine. Good method, generally with all styles of play when in combat, keep moving. Wards will protect you if you time them correctly, just make sure you use the correct ward to the correct opponent, a lesser ward against a High level Pyromancer will not end well.
The best advice I can probably give, make sure if you favorite spells which you probably favorite a lot of spells. Make sure you select the right one when you attack, believe me I know how badly it ends when you attack a Bandit Chief with Magelight instead of Thunder bolt.
