I'm a vampire and I absolutely love staying in level 4 at all times. It makes me feel like monster knowing that everyone hates me, but inside they fear me. Role play aside I also like the power from it.
However, as I'm sure you know, it's extremely difficult to visit your Whiterun house without having the entire town murder you.

Could I find a shack in the woods somewhere nearby, maybe near Riverwood, and kill everyone inside and make it my own? My only worry is that storing my stuff in those chests will have them disappear. Can anyone confirm if this will work?

Also, I am aware I should find a house with a roof haha. Would be pretty bad to fall asleep and have the sun burn me mid-slumber.

The perfect place for you http://uesp.net/wiki/Skyrim:Anise%27s_Cabin

You can steal the alchemist shack. And that house with the psycho Dunmer in it.

Pretty much any of the shacks outside of towns are fair game, just don't use the crates.

theres also http://uesp.net/wiki/Skyrim:Abandoned_Shack
plus its gory inside, just what a vampire needs.

Not really. I did in morrowind, like in every town, but in Skyrim beds are owned and loot boxes/bags likely wont have what you store in them.

Yes, if you exploit a glitch in the game.

Absolutely brilliant! Thank you!

Do you know if my things will remain in the chests?

I think you can basically claim a house if you kill the owner but because the chests respwan I wouldn't use them

Why did I think about how much it would weight and what type of vendor would buy it?

From what they've said

It's located in the basemant, not the one on the main floor.