Man the house in Whiterun sucks, it's so tiny. I've got a huge pile of Dragon Bones and Scales in the Alchemy room, my table is full of spare weapons, my bed is full of spare armor, now I've got nowhere to put all the loot I've been finding.
Gonna need to make Solitude my hometown very soon, hope the house is worth that 25K...
EDIT: I've still got 4 of the main cities that I haven't even visited, maybe I should check those out first...
If you go to the far end of the first floor and go in the door to the left there is a chest on top of a closet. As far as I can tell there is no limit to how much you can put in there. Or it's very large if there is a limit.
Edit: the chest is in the first floor bedroom. Right when you open the door.