I was wondering what class you would call the character I'm currently playing. I have a level 19 Redguard who's skills are: Illusion, Alteration, Destruction, Sneak and One Handed.

Right now, I have him wearing some buffed Fur Armor but once I get the Alik'r Garb I plan on wearing it but keeping light armor boots/gloves so should I invest any perks into Light Armor, or just take the Mage Armor perk in the Alteration tree? Would the perk even work while wearing LA boots/gloves?

Those skills would certainly fit a Nightblade
If you wear any armour at all the Mage Armour perks won't work
There are a couple of items of clothing that have an AR. They don't count as armour and the perks will work with them
You could also take the Lord birthstone. That gives you 50 AR and 25% resist magic

There is a machinima director on youtube its like trendtokill i think he has class setups:}