as the title says i am going to start a destruction mage and i dont know which path to choose fire,ice or lightning?

If you want to specialize solely on destruction magic, you should choose all three of them. You can stop heavy melee enemies by depleting their stamina with ice. Shock is good against mages because of the magicka damage. Fire is the most damaging out of the three, and many creatures of Skyrim have a weakness to it.

I want to choose only one

You are definitely setting yourself up for a difficult game, and theres nothing wrong with that if you find it exciting and fun. Have you thought about going strictly conjuration? It will allow you to stay within one school much easier and gie you a wider range of tools like bound weapons and different conjuration elements (atronachs) for different situations. Are you planning on using any restoration or relying on alchemy and potions?
Personal preference for me would be Fire Mage (mainly cause of the extra damage they take) with all the fire perks like incineration, and to avoid the restoration tree I would invest in alchemy, with some perks in enchanting to make some good mage gear at later levels.

EDIT: I wold think storm mage would also be pretty effective (maybe more then fire?) for most mobs considering mages are a pain and shock would go a long way with those guys.

Then make it lightning... only one creature in the entire game is immune to lightning, and that is the storm atronach. You pay for this convenience by needing more magicka to cast lightning spells than the other elements. Also, if you are on the PC, I very very strongly recommend that you download a mod that balances the magic system.

-Loth

Good to know, I had a hunch that lightning was a pretty un opposed force, I may try a storm mage myself now hmmmm......

I'm playing one... after trying out the other elements, the lightning side is doing better than the others. A lot of monsters (even NPC dunmer/nords) have fire/frost resist, and the projectiles are hard to aim against a moving target. Lightning is pretty much the only spell that can hit a dragon in mid-flight, for example.

-Loth

Ah yes dragons, that tips the scales a bit more for lightning. You wont have to wait to see what they breath so you can equip the appropriate skill, just shock em since there is no shock element dragons. I think I will be restarting my mage character now lol

ok thank you all i will try lightning