I'll start then:

Finding the balance.
So I didn't put any effort into enchanting because I feel that it would lead me into becoming way too powerful as a Mage and I don't want that.
Finding, earning or buying gear with enchantments is good enough for me.

What if you meet a enemy that is hard to kill?
Well, when I feel my destruction spells isn't strong enough I will use one of my 'Fortify Destruction' potions that will work for a short period of time.
It does give a nice boost in damage when you feel it's needed but it's very situational\optional. Not permanent! And that is a good thing when you want balance.

But I still have not decided if I want to put any points in Alchemy for potions to get stronger.

What if there is a lot of enemies?

I will not use Conjuration to summon elemental, demons or whatever. Because I think that makes everything too easy.

But occasionally I could raise a dead human that I've killed. Just for a short time and not permanently.

Also there is Illusion that I use a lot for situations I don't feel I can handle. So charming my enemies or making them run in fear works well when needed.

And you know, each perk on each school you focus on is optional so if there is a perk you feel that would make you too powerful, don't take it.

If you want some balance, that is.

So how do you become a Mage that isn't too powerful or too weak?

Please do tell, from your own experience\imagination.

for one thing, i dont dual wield destruction or get the impact perk.

Not only does that make it too easy, but it makes the game boring. It turns every battle into "hadouken! Hadouken! hadouken! etc." until the enemy is dead.
Makes dragons easiest battle ever cus you just keep hitting them with a dual fireball, they get knocked back, by the time they recover, you already hit them with another fireball and stagger them again

I also try and use my skills evenly and have them level up the same, but i always find myself getting destruction and alteration to 100 while illusion, restoration and conjuration are still in the 40s and 50s, no matter how much i use the other schools.

Illusion levels slow cus like 70% of enemies in skyrim are undead draugr that illusion spells dont work on so i cant use it as frequently as i want.
Conjuration just levels slow, and with the new patch i gotta cast summon like 5 times for it to work once so i rarely use summoning anymore cus i get myself killed trying to use it. (reanimating corpses is almost as ineffective as 8/10 of my zombies when ressurected will just stand there walking into an invisible wall not attacking anything)

And restoration is like the slowest skill in the game to get up, no matter how much you use it. For example, i stood on a trap that shoots fire a t you, letting it hit me first by using healing spell, then trying a ward spell, and it took literally like 10 minutes of constant flames hitting me while casting restoration spells to level up once.
Wheras in comparison, take alteration and telekinesis, pick up a book or something and watch your alteration skill climb like 20x faster then your restoration skill..

Pay a mercenary for some assistance when you know you are going to fight the undead, because http://elderscrolls.wikia.com/wiki/Courage is a Illusion spell that works fine on humans.
I usually have Lydia with me and that works well. No problem with keeping my Illusion school up with the rest thru ordinary use.

Illusion is very easy to level in my opinion. I use muffle and invisibility for sneaking, and calm/pacify on people and animals and it levels up very quickly. Once you get the Master of the Mind perk, all the illusion spells work on undead and machines. I'm happy having muffle and invisibility, which are very very powerful and useful spells.