If I use a combination of light and heavy armor, say fur armor but iron boots and gauntlets, which skill will be leveled? Both or just one? Also, what effects how quiet your movement is when wearing a combination? I know heavy armor is louder, but does it get any quieter if you are only wearing a few heavy pieces?

It depends on where you get hit. If you get hit in the foot and you're wearing fur boots, then you'll get a light armor skill up. If you're hit in the chest and you're wearing steel plate, then it would be a heavy armor skill up.

That's a really good question about the sneaking, I have no idea but would like to know as well. Anyone?

I don't think anyone has broken it down yet, but each armor piece has it's own "noise" level for sneaking, which is directly proportional to the armor's weight, so the heavier armor pieces will make you noisier when sneaking.

If you are going completely by stats, light armor is superior, since you can hit the armor cap with dragon scale armor, even without using exploits and still have all the light armor perk and sneak advantages. The Muffle enchantment should help if you like to mix and match armor types along with sneak enchantments if your sneak is not up to 100% yet.

http://www.uesp.net/wiki/Skyrim:Muffle_%28effect%29
http://elderscrolls.wikia.com/wiki/Muffle

Thanks for the answers. I wasn't aware that each piece could get hit separately. This should help with my new character.

I don't know about that. There is no locational damage in the game, so I am not sure how the game would know which armor piece took the hit. Perhaps it is just a proportional allocation. In other words, if you are wearing just a Heavy Armor Helm and the rest Light, then you get 20% of the hits allocated to Heavy Armor when hit anywhere.

It would be good to see the formula for this calculation.