I am a level 11 warrior build in Skyrim and I was wondering what armor type I should use... I started out using light armor because I have a shield and I didn't want to be weighed down by heavy armor, but now I know that you can eventually make each armor weigh 0. I was thinking that maybe I should start using heavy armor now and that it would be a better choice in the long run. my light armor is 15 levels higher than my heavy armor now, but I only spent one point in it.
It honestly does not matter. It has been proven many times that any type of armor can actually max out the armor caps with just 1 or 2 perks in their respective armor trees depending on which armor you want to use (maxing out leather or iron takes a bit more perks/enchants than say daedric or dragon).
They really do give you the ability to play any way you want and to remain viable. The link above shows the minimum perks needed to max out each classification of armor so you can pick what you want to look like and aim for that end goal.
if you want to have little damage then just use heavy armor and the steed stone: fortify carry weight and your armor weighs nothing so like that you can use and train heavy armor without being slowed down.
or just level up more stamina and use a 2 health to 2 stamina ratio. it also depends if what weapons you use because two-handed does more damage but slows you down because of its weight.