I personally always prefer wood over carpet. You will want to match the wood that you already have. You can find a large area rug that will compliment the wood and work well with your sitting area. You might look for a 12' x 15' which is a standard size.

Thank you for your suggestions. I appreciate it

If budget allows, run the hardwood into the sunken living room and then find out how you want to deal with area rugs at a later time.

Here are some other great options besides hardwood and carpet.

http://www.momodwellings.com/single-post/2016/07/08/Bamboo-Isnt-The-Only-Inexpensive-Eco-Flooring-Option-7-Affordable-Sustainable-Modern-Floors-For-Your-Home

I would prefer any hard surface with a rug over the wall to wall carpet. I think continuing your existing floor would give your space a cohesive look. One caution if your wood floors match your existing floor, the step down could disappear in some lighting and be a fall hazard. Do look into lighting or banding, something that would make the change visible.