I can see you've got great advice from Ashley and everyone else xD still, I'll throw in my 2 cents.
-As a pure Mage, I don't like wasting perks on anything not in the magic side of the perk trees. That includes weapon and armour choices, supporting skills (like speechcraft, lockpicking). If you like Illusion, then Sneak is a good choice because of the Quiet Casting Perk.
-As my own choice, I don't like having more then one crafting skill (Alchemy, Smithing and Enchanting) because the game gets too easy, so as a Mage, I would say, go with Enchanting (so you can create gear that reduces the cost of Magicka of your favourite school of magic). Now, if you don't have any restrictions about that, get Enchanting and Alchemy, both are great for mages.
-Don't go all over the place. What I mean with this is, plan your character. Let's say, you like using Destruction, Conjuration and Alteration. Why perk Restorarion all the way up to Master if you don't plan or rely using it to Turn Undead? Close Wounds is an awesome healing spell in the Adept Level, so don't go past that if you don't need Guardian Circle to turn powerful undead. Also, notice you have 1 offensive school and 2 support ones in the exemple I gave? So, you don't need Illusion. At least this is how I play, I always get Destruction and 2 support schools. Of course you can pick more skills, but you will need more levels to perk them up.
-Do NOT have any gear that has Absorb Magic effect if you use Conjuration. This effect WILL absorb you own summons, which means, if you have 100% absorb magic, your summons will never be summoned (100% of the time they will be absorbed). This also counts for The Atronach Stone.
-Standing Stones to use: I start with The Mage to get to a point i feel comfortable with my skills (usually 100 on Destruction or Conjuration) then I change around. Sometimes I use the Steed for carrying more stuff without the need to invest in Stamina, but The Lord is the best imo, because it gives you more Physical and Magical deffense, which is always welcome.
-Shout: I love all the shouts in the Dragonborn DLC, and on the vanilla game, I'd say Become Ethereal is my favourite, since you can literally jump down from mountains for quick traveling on foot, and you are imune to the sun if you are a Vampire and use it.
-If you pick Alteration and use Flesh spells, DO NOT use any kind of armour, including Dagon Priest masks, for they are stronger that way.
-If you pick Destruction, I would say get two spell branches (I usually go with Lightning because nothing apart from Storm Atronachs are resistant to it, and Fire OR Ice, but not both). I do this to conserve perks, but again, if you want to get them all, there is no problem at all. Do what suits you better.
-Have fun! You are playing with a really powerful class once you get used to it. At high levels, you can kill an Ancient Dragon without being hit at all, just stun locking it with the Impact Perk.
This is all I can remember from the top of my head. Hope it wasn't too confusing and it helped =P