I just created a character and i decided im going to use a staff as my main weapon,right now im using destruction spells to lv up that skill up so that when i do use my staff,the charges deplete slower.Also i think the higher my destruction skill is,the more powerful my elemental damage enchantment will be ,am i right on this?Also i wanted to know if magic perks apply to magic that i cast with a staff,say for example i unlock a perk that gives me a damage bonus for fire spells,or a perk that make my restoration spells heal more hp,will that perk bonus apply to say a fireball or heal if i cast it with my staff?

My understanding is that your level in destruction would have no effect at all. Your level in the enchanting skill will determine how many uses you get before a staff is depleted, and how much recharge you get from soul gems. A particular staff will always do the same amount of damage... I think it's 8 for a staff of frostbite or flames (+ the fire bonus if the target is already on fire) or 50 per second for a staff of wall of lightning.

You may want to double check that

Okay, I double checked it...

http://www.uesp.net/wiki/Skyrim:Staves is the uesp page giving staff damage and it doesn't indicate any changes. The only exceptions I presume would be if the target has resistance or weakness to a particular type of effect. A nord bandit for instance would take less damage from a staff of frostbite, but the base damage of the staff would always be the same before any such resistance s added or subtracted.

Indeed, UESP doesn't mention that all destruction magic effects, including staff enchants, are under the destruction magic school and therefore, subject to all damage augmentations: perks, Shalidor's Insights and ofcourse, fortify destruction potions.

I dunno, I've never noticed it effecting any staff I ever used... which would explain why I stopped using staves a long time ago. At low levels they are fine, but once the higher levels are it, it takes an act of congress to kill anything more deadly than a wolf with a staff unless it's something like a staff of ice storms, or lightning wall.

You may be right, but if you are, it certainly isn't obviously so.

Try it ingame. You'll see.

And when you stack it with the rest I mentioned, you'll see even more

The higher your level In whatever magic you're using, the stronger the staff. It even says it on the loading screen sometimes.

The higher your Destruction skill, the more uses you will get out of weapon or staff enchantments that fall under the magic school of Destruction. Also, perks like Augmented Fire will increase the damage of staves or weapons that use fire magic. In an unmodded game, that is. Better Magic for example disables the damage increase not only for weapons, but also for staves.

Edit: I guess the same thing is also true for other magic schools. Higher skill-level nets you more uses without having to refill them with soul gems. Perks that increase the magnitude or duration of the effect will probably apply as well.

Yes, destruction boosts will affect staffs.

A staff of incineration will deal 112 damage per hit (EXCLUDING afterburn) if you have augmented flames 2/2 and you're wearing the ahzidal mask.

Check the "Notes" section regarding governing skill information.