Ideally, I'd like them all maxed out so I don't have to choose... but I'm not sure that's possible either. Especially if I want to enchant as well.
My destruction mage build up to level 49 is below. I have most everything perked out except Alteration. If you are good at keeping your distance, using terrain and dodging arrows you can play a robed mage without bothering with mage armor. There are also ward spells.
A lot of folks say wards are more hassle than they are worth, and there is truth to that. A good shield bash (even unperked) will interrupt a spell and stagger an opponent, so all in all, shields seem more useful than wards, but I wanted to have a character that relied on wards and it seems to make sense for a robed mage, ao I took the Ward Absorb perk. The respite perk in Restoration is also really useful.
If you do perk Alteration, beware the Atronach perk because it will affect your ability to cast summon spells. There is a bug that makes summoning spells get absorbed as if it were an enemy spell, so when you try to cast them nothing happens 30% of the time if you have the Atronach perk. The same thing happens with the Atronach stone, but you can change the stone. The perk is permanent.
In Conjuration, I went the necromancer side because it is fewer perks to twin souls and because there is a bug in Elemental Protection on the summoning side that breaks summoning staves.
I have 9 points in illusion so I can cast those spells on higher level opponents. Without the illusion perks, you will eventually reach a point where most of the enemies will be too high level to be affected by fear/calm/frenzy. With the perks you can dual cast an expert level spell to affect enemies no matter what their level.
I put 7 points into alchemy so I can make good fortify destruction potions and so I can fortify enchant for stronger enchantments. Although it is a "stealth" skill in Skyrim, historically it was a magic skill.
Opinions differ on the Intense Flames/Deep Freeze/Disintigrate perks. I am taking them because they have cool effects and you can feel like a powerful destruction mage when you cause something to disintigrate, plus it cannot be raised by a necromancer if you turn it to an ash pile. The Intense Flames perks may just be more hassle because you then have to chase a fleeing enemy down, but I figure that just adds to the fun.
I took the dual casting/impact perks but I rarely use them. Impact staggering everything is no fun. I mostly use dual cast impact on bears and sabrecats. But I was having an extended battle with a Cryomancer before I had made any fortify destruction gear. She was at the bottom of the stairs and we were trading spells. It was a stalemate because I did not have enough magicka to finish her off and she kept healing. I refused to chug a bunch of potions, so finally I just waited for my magicka to regenerate. I had to stick my head out every once and a while to give her a target for her ranged spells so she wouldn't rush me and then dodge back into the doorway before she could hit me with her ice spikes and ice storms. Finally, when I had enough magicka, I charged her dual casting lightning bolt. I had enough magicka to get the spell off three times and managed to hit her all three times and ended the fight, so dual cast saved my bacon that day. I play with no crosshair, so hitting things with ranged spells can be a fun challenge, especially with other mages who tend to move around pretty fast.
Have fun with the mage play. I was disappointed at first with Skyrim magic because there was no spellmaking and they deleted a bunch of spell effects from prior games, but even so, it is still fun to play a mage in Skyrim.
Illusion 9 Novice, Dual Casting, Animage, Kindred MageQuiet Casting, Hypnotic Gaze Aspect of Terror, Rage, Master of the Mind Conjuration 4 Novice, NecromancyDark Souls, Twin Souls Destruction 12 Novice, Dual Casting, ImpactAugmented Flames (2), Intense FlamesAugmented Frost (2), Deep FreezeAugmented Shock (2), Disintegrate Restoration 5 Novice, Respite, RegenerationNecromage, Ward Absorb Enchanting 11 Enchanter (5), Insightful, Corpus, Extra EffectFire, Frost, Storm Enchanters Alchemy 7 Alchemist (5), Physician, Benefactor