I happen to think baskets of yarn laying around is a gorgeous cozy look, so I plan to buy large baskets (I find really cheap ones at Value City Department Store, Walmart, and on clearance at the local craft store) and display my yarn...
So far I have a well positioned basket right near everywhere in the house I might want to knit (after 3 weeks!) organized by color family so they look pretty and on purpose. Primary colors in one room (where my decor happens to have primary colors - the office), pastels in another (which works in my bedroom) and deeper colors (black, dark blue, heathered gray...in the living room). I've been keeping current projects (so far I have 2) in the bedroom basket.
I admittedly don't have a lot of yarn yet, but when I do, I'll use this system until I can't anymore.
I also don't have any dregs. When I have some, I'm thinking a small hidden away covered container the size of a bread basket might do.