So, I just started playing skyrim for the 1st time, and I am a Altmer mage. I am having a really good time, but I am running in to a huge problem. Armour. I am literally using the same Armour that you find in the Helgen tutorial, because I can't find anything better. So what I have found from my basic research is that I should enchant some sort of clothes or armor with 0 defense (so I can gain the boost from the Mage armor perk) with enough enchants to make 2 schools of magic free. So, how would I do that? Also, is it even worth trying to get the bonus by wearing no armor, or should I go for light armor instead?

Thanks in advance!

Welcome to the forums. Depends on what type of mage your going for. For a battlemage I usually go with light armour and for a pure mage I go with robes. If this is your 1st playthrough of the game I would suggest playing as a battlemage and try to find/buy a set of light armour which you can then of course upgrade and enchant to reduce your magic costs and maybe also increase your magic pool.
Choose your perks carefully especially at the start of the game and try to create a fairly well rounded character especially in the magic schools. You need to get to the College of Winterhold as soon as possible as a mage where you can develop your magic skills and strengthen your character and also regularly visit a blacksmith to keep your armour up to scratch for the many enemies you will encounter in your travels.
All the best with your playthrough and if you have any problems there are many members here who will gladly offer you advice. Good luck.

I am trying to be a pure mage. I did join the college, but what combo of enchants would I need to make spells free?

well, from a PURELY mechanics perspective cloths actually give no real advantage over light armor (Which is nearly as light), and the best Armour spell only lasts for a short time and takes A LOT of magicka. The best robes have enchantments that besides the archmages robes are weaker than stuff you can enchant. even the archmages robes are beaten by focusing on the one or two magic types you want and enchanting stuff to make sure you decrease casting costs there, since 10% to everything is not ALL that great.

NOTE: for those who say "not lore friendly" or "then he is not playing a pure mage by my standards", daggerfall and battlespire has mages able to wear leather armor and many of the NPC magic classed NPC in all of the games have light armor.

max out your enchanting, and then enchant 4 or 5 peces with "fortify *whatever magic school you want*" you can only do it with two, maybe three schools and then that means you are not focusing on other stuff, but you can easily do it with one school of magic that you use A LOT like conjuration or destruction

The first time I played as a pure mage in Skyrim I was fine with the Archmages robes and remember really enjoying the play style, so much so that it's what I mainly play. I wouldn't worry too much about trying to get 100% spell reduction as if you approach the pure mage play style correctly you don't really need it. As it's your first playthrough of the game I'd suggest not to make things to confusing for yourself as the pure mage is not the easiest play style although it is great fun once you get used to it.
Have you completed the COW questline yet?

If you choose cloth, I advice to make use of conjuration. Summons will take the attention of your opponents and make it easier for you to keep your distance.

Correct me if I am wrong, but I thought if you duel cast + stability + vampire necromage, you can get the spell to last 2.5 mins (read on the wiki) If I have robes with fortify alteration, can't I basically be permanently at the armor cap? Also, wouldn't creating light armor require a lot of investment in smithing?

yeah, possibly, but it would not work on the PC with the unoffical patch since teh necromage thing is a bug. Also, it would require you to become a vampire, which, without mods, has no real advantages compared to just being a regular mortal.

Fortify alteration only decreases the cost and nothing else, and even then, the spells costs A LOT.

You do not have to create light armor, you can find it and enchant it perfectly fine and still use alteration to be at a similar AR rating at less the cost and without using those three perks. Smithing in and of itself is a great idea no matter what kind of character you are anyway since even with mages you can craft daggers and stuff or craft gear for your followers.

I tend to do heavy armor for Battlemages and normally up to Ebony. (Dawnguard armor for Paladins). Normal mages would be just no armor and only use the armor spells.

I honestly don't get how it is a bug... Necromage specifics that all spells do more power on undead and if you are undead yourself, then self spells would do more power on you anyways.... Right?

that is going by the "letter" of the descriptions. it being in the restoration school, which is about healing life, turning undead, etc it seems REALLY obvious that the "spirit" of the perk was meant as an anti-undead perk and not meant to be anything to help the undead.

Understandable but still I feel technicality wise, it should work like that normally, even lore-wise (not as a glitch). But I guess that's just me... I tend to look at things differently anyways.

Note: I don't count game-mechs as lore in the first place anyways, I just saying more as an example.

Better?

HOLY WALL OF TEXT BATMAN!!!!! Could you PLEASE edit it to make it readable, it hurts my eyes just looking at it. .o:

I'll try to keep all the posts Twitter size from now on. It's my first time on this forum so I wasn't sure what's allowed. I'll make sure to report any posts that don't have perfect spelling and grammar. I can see that's how they do things on here. If anyone needs advise from now on I guess only long time members are allowed to give it. I can see this is one of those type of forums. I thought this was a friendly forum, but it's going to be just like You Tube. Sorry if I offended anyone. Why are you typing in all caps and shouting at me? I thought your only suppose to put one exclamation at the end of a sentence? !!!!!!!!!!! Why is PLEASE in bold? Why a face in the text? All of those grammar mistakes would be an F for a grade in school. Now me on the other hand I don't really care what people type as long as I can read it. I don't understand how some one can be such a Grammar Nazi then use poor grammar himself? I don't understand why I deserve to be attacked for trying to help out someone. If you can't read it then don't reply. Just block me. I'll just talk to friendly people that aren't so anol. This forum is for advlts, right? I'm not sure why we need censorship for an advlt forum for an advlt game? I'd like to stick to talking about the game rather than getting into petty disputes over petty stuff. If you don't like what I type don't read it. Sorry to Blazzer3333 I did have answers to your questions, but someone was unhappy cause it was too long and had spelllllinnng & ,,,,,grammmmmm?!!$*%er .... errors. OOPPPS. Hold on let me find the edit button. Sorry if you can't read that. I'm a little upset after the rudeness.

Well to start off your going to need to join the faction "College of Winterhold" and do that questline along that you get these two items.

-Arch Mage's Robes
-Morokei

The Arch Mage Robes give you three following enchantments: All spells cost 15% less to cost, +50 Magicka and Magicka regenerates 100% faster. Next Morokei gives you one enchantment: Magicka Regenerates 100% faster. So that is 200% faster Magicka regen and a lot of other great bonuses those are the two items I highly suggest you get if your going to be a pure mage. Good luck friend and welcome.