HI Steve,
Thanks for all the pictures- that really helps me get a sense of your space!
For starters, I'd paint the walls, ceilings, and baseboards in a creamy warm neutral like Sherwin Williams 7547 Sandbar or 7567 Natural Tan. This will basically make the ceiling disappear, soften the angles of the architecture and draw your eyes to the woodwork, furnishings and artwork you've so carefully selected. Paint the walls and ceilings in a flat finish with the baseboards in satin. You may find that paint is all you need for a completel transformation.
If you're set on changing the family room floor, I'd go with a similar color carpet but look for a sublte geometric pattern to work with your modern look. The Perfect Rug (www.theperfectrug.com) offers two great choices- Exotic Coverings in Safari Beige and Grand Safari in Cracked Reed. They'll create a rug for you in any size/shape, but call to find out if they'll sell yardage to installed wall to wall.
I'd only recommend putting hardwood floors in the family room if you're willing to change out the kitchen and hallway floors too. Otherwise you'll make your two room look smaller and more crowded. If you ready that big of an investment and change, look for medium tone woods that are darker than the walls and lighter than the cabinets. Stay away from red tones (they'll only fight with your existing cabinets and wall unit) and look for ashy blond or walnut brown colors.
This photo has a stone floor, but you'll see the effect- create a neutral backdrop for modern lines and beautiful materials. Hope this helps!