Basically what I do is depending on how many enemies their are, is that If I am in sneak mode, I will use the frenzy spell if there are a few enemies and I am not spotted. Then go to a dual casted flame cloak, and fireball in one and flames in another. If I am spotted, then I conjure a helper, cast flame cloak, and then dual cast fireball or firebolt. When I am going down the road or over the hill, I keep a summon frost atronach or fire atronach in one hand and flames in the other so if I am caught by surprised I am ready, then after the conjure spell I go to the flame cloak and then back to the atronach spell.
I use only destruction, illusion, conjuration and restoration along with alchemy and enchanting. When ever I am going down the road or over the hill, I am always going slow and looking around for enemies and I usually spot them before they spot me. I also use shouts to help me. I travel with no companion, except in the very beginning. I do not use alteration for I do not like it. I do not wear armor, but only robes that are enchanted from the college or enchanted by my character. I have never put points into health. Only magicka and stamina, at a rate of 3 health / 1 stamina, for stamina helps with carry weight.
My gals are over level 45, some over 55 and still going strong and the only real problems I have is with dragon priests. I have no mods, for I play on xbox and I have no problems with destruction. It depends on the perks you take. In destruction, the ones I take are augmented flames 2, impact, dual casting, intense flames, augmented frost 2 (only for fire dragons) and the master perk. In illusion I take everything but dual casting. In restoration I take recovery 2, regeneration, necromage and up to adept. In conjuration I only take the major perks, novice to master, and then mystic binding.
In Skyrim it is not how many time you hit an enemy with a spell that counts, but how much damage you do with a single spell that counts. I also only use the mage stone, and I always rest for at least 1 hour before going anywhere, and if I see a bed along the way, I also sleep an hour there. The higher you get in destruction, the better your spells, the stronger your spells. I very seldom use shock type spells, mostly fire spells, and frost only against fire dragons. I do not use wards, mage armor, or any of those. Just go slow, conjure a helper, use a flame cloak and burn them. I also play on adept, wear robes or cloth armor that my gal enchants, and I have very little problems with any enemies, except the dragon priests.
Hope this helps.
Here is a link that might also help.
http://www.gamesas.com/topic/1481463-never-actually-made-a-mage/page-4