Let's say that I use destruction as primary skill with Illusion, so should I wear archmage robes or the Master of Destruction Robes, I mean which is more beneficial in term of flexibility? Also, does anyone know if there is any nice enchanted robe I can get early in the game without having to buy.

The Archmage Robes are not as flexible for somone who is planning on swapping outfits to boost skills throughout thier game. The Master Robes can be used in conjunction with Enchanting to reduce the casting costs of many schools of magic - I do not like free casting, but reducing the Mana cost of a spell for three different scools of magic is not abusing the game mechanics.
EDIT Joining the College of Winterhold will get your character a decent set of Robes for free.

Okay, so does that mean the Master Level robe for any school of magic can be modify to be able to reduce casting cost for all school of magic? Also, is alchemy a must for a pure wizard?

I'v gotta question, has anyone come across a master hood? I'v seen novice, adept and so on but no master one...

I personally preferred the Masters Destruction Robes since my mage used only destruction and conjuration. Conjuration did not require enough magicka to warrent losing the benefit of the Master Destruction Robe since I rarely reconjure during a battle and potions are enough to fill the bar if I do. I was able to use Destruction robes along with my other gear to get incenerate down to only 15 magicka. That was without using enchanting. All my gear was found or purchased from vendors. However if I was using all the schools of magic I would highly consider going with the Archmage robes since they do reduce magicka use for all schools. I don't like the idea of constantly switching gear during combat. It is a major inconvenience considering how clumsy the menu system is, and I don't like that many interruptions during conbat.