Use duel casting or magic and staffs, magic and a sword, axe or mace, or unique dagger if you have to.
Also you can use a shield and magic. The shield of Perydrite, Spellbreaker is good for mages, it deflects magic. Also good is Ysgrammers Shield.
I always carried a shield and at least one sword.
You can also have the option to use sword and shield then. It does happen if a enemy requires 'mage punching' tactics.
Mage punching is when you have a mage who is strong and magic can't get close to, but is lightly armoured. Then the best thing to do is charge in with your strongest melee weapons, or weapon and shield and bash them to death.
You can also use shield and staff.
Put most of your points into magicka. But not all. You need some in health and stamina.
Pick 1 main school and a secondery school.
You can do them all, but you have to focus on one main and one secondery.
My mage was destruction main and conjoring secondery.
You should have destruction spells whatever you do, because they are very useful. And a lot of fun.

Definately join the CoW. You can become archmage and get some awesome robes.
Always buy spells, never rely on loot, only the basic stuff is in loot.
You can use robes, light armour or heavy armour.
Mine wore robes or heavy armour for hard fights. Robes mostly.
I would say robes and light armour is best.
But keep some enchanted heavy stuff about for hard fights.
You don't even need armour sometimes. I enchanted fine clothes, boots and gloves.
I changed to thalmer gloves and boots for combat and formal.
I constructed a outfit made up of the archmages robes, thalmer gloves and boots and the mages circlet.
The Armour Of The Old Gods set is awesome too.

Enchant you boots with stamina enchantments, it helps when running away from fights or till your magicka recharges.
Personally, I think mages look the best most of the time, because the outfits are mostly good looking and flattering.
Be careful with followers, because some walk straight into your attacks.
Lydia is the worst.
It is easier to not bother with followers at all, because sometimes you kill them by accident, a lot.
I did'nt bother with followers most of the time, apart from Vorstag.
He is the only one who works properly all the time as far as I can tell.
If you have to fight with people, use focused spells and a sword or staff more. If it get's really bad use all weapons.
If it gets really bad, and they die or go down a lot, use healing hands and a staff or melee weapon.