If you are going the pure mage route, then the general guideline is to invest heavily in Magic.
Stamina is for running and special attacks with weapons.
Since you will be casting spells in light (or no armor), stamina has very little use for you.
Try investing in a horse for those long runs.
Health is something that you can invest in if you feel you die too much.
However, there are significant number of protection spells in Alteration (Skins) and Restoration (Wards) that you should have ample protection with your magic alone.
Also remember that you can permanently stun an opponent with destruction dual cast perk "Impact".
So that leaves dumping the rest of your points in magic, allowing you to cast spells more often.
Remember though, that investing heavily in magic makes it harder to make a "hybrid" character in the later levels, once you've maxed out your destruction tree.
gaming.stackexchange.com/users/4393/Resorath
My recommendation would be building your magika to 300-400 ranges then putting the rest in your health.
It is good to have a bigger pool of magika
but it won't do you any good if you cannot live through the fight and not having enough magika regen by your clothing enchants will leave you with an empty magika pool.
EDIT(To rephrase): "There does not seem to be any explicit penalty for spellcasting in heavy armor.
However, armored mages do miss out on the magicka regen and spell cost reduction provided by robes.
At higher levels, the Enchanting skill can be used to place these effects on armor.
In addition, a three-perk commitment to the Restoration tree increases Magicka Regen by 50%.
This perk requires a higher level and perk commitment, but also negates the inferior defense of most robes."
--- Start out with robes then move to light armor with enchanting.
gaming.stackexchange.com/users/18818/Zero
I learnt the hard way that for a pure mage, investing in health is best.
But yet, this is because I'm willing to exploit Enchanting.
My first mage had 500 magicka and 200 health and 100 stamina.
I was getting one-shotted as my enemies leveled up with me.
The game just kept growing harder, and I was forced to sneak about and plan too carefully every tiny encounter in every dungeon.
The bears and saber cats were the worst.
They come up from behind and with no armor to protect me, I'm dead in one bite.
My second mage however, concentrated on collecting soul gems (steal, buy, whatever is necessary) - filling them with souls, and enchanting weapons with "Banish".
I brought my magicka to 150 and put every other point into Health.
Selling all those weapons made a mountain of gold, and once I had all the right perks, I enchanted Robes and jewelry to grant free magicka in every school of magic.
I mostly don the free conjuration/destruction gear, but when I need to cast a particulary expensive alteration/illusion spell, I wear the clothes for those schools.
That, combined with Impact + Argis the bulwark in some decent ebony armor, made my character quite unstoppable.
Any fight with me spawns a couple of dremora (twin souls), and I stun the archers and mages who fight from the background with impact (many times one-shotting them) - I also like the Bound Bow when I sneak for fun, and sneaking is easy because I wear no armor.
gaming.stackexchange.com/users/16125/Aditya M P
I put it all in Magicka until I start feeling squishy, then start putting it in health.
Watch out for the leveling tiers (10,20...)
when the NPCs get harder, but for a pure mage, you only need enough Health to avoid getting 1 shotted, but you can never have to much Magicka.
Of course, Alteration's _Skin spells help you survive with less, so they're worth it in the long run.
Magicka always recovers faster with a Mage character, especially if you invest in Restoration.
I only use Wards against other Magic, especially Dragons, but once you get to Ward Absorb, you can use it to power destruction spells.
So in answer to your question, the ration is as much Health as you need, the rest in Magicka, and Stamina is for fighters.
If you're really worried about it, Redguards make great spellswords, and can sprint indefinitely for a madminute with their racial power.
You can also enhance you stats with the Gaulder Amulets, and Rahgot if you really want Stamina.
(No mage should need more than 200 stamina.)
gaming.stackexchange.com/users/28065/Psiberzerker
Enchanting (and sometimes smithing) can substitute for any shortage of stat points.
A suit of legendary armor enchanted with resist magic will make you nearly impervious to damage (with the exception of poison and fall damage).
You can also enchant your gear to give you free casting of any school of magic, removing the need for a large mana pool, provided you're willing to stick to that school or swap equipment accordingly.
A weapon of drain stamine will make sure you never run out of stamina in combat.
Personally, I prefer a large mana pool and some health (~300 health or so is good at later levels) + damage nullifying gear, to avoid the tedium of swapping apparel to cast expensive spells.
gaming.stackexchange.com/users/19827/kotekzot
I may be speaking for myself, but I honestly wouldn't put much emphasis on Magicka.
Now before you throw the downvote button hear me out.
As someone who invests heavily on enchanting, and alchemy, it is entirely possible to achieve 100% Destruction Magic Magicka reduction.
In short, spells will cost you absolutely nothing.
Stamina would be great for running long distances (along with Healing perk to allow you to restore Stamina), but I would focus on Health a bit more.
I've overhauled the game battle mechanic to make it extremely difficult,
as a result, health is crucial.
But these are just my thoughts.
gaming.stackexchange.com/users/30951/Stupid.Fat.Cat
As a mage, I've put every single choice into magic, but I'm wondering how often I should be leveling up health or stamina.  Is there a good ratio to follow?
Which is best stat to level up when playing mage: health, magika, or stamina?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/48159
gaming.stackexchange.com/users/18817/hvgotcodes
Invest heavily in magic. Build up to 300-400 ranges and put the rest into health.  The most common belief is that as a mage you should invest in magicka but few other players tend to believe differently.
It is described that investing in magicka gives the best results. Players believe that investing in health is better.