Could you just go with a 9x12 wool rug (they tend not to have backings and wear so well) then get the felt rug pad?

They have thicker felt rug pads. You can move/shift a rug on a felt pad, but once you have all the furniture on the rug it will stay in place.

Have you had wood floors (site finished or engineered) with area rugs before?

The wood floor areas that are not covered by the rugs will fade. It starts to happen quite quickly.

I try to minimize the fading by having light filtering blinds and closing them when the sun is coming into those rooms. I now have wired/automated blinds, so they automatically open/close at the right times of day and I don't have to run around the house doing it myself, or it not getting done at all if I'm away from the house.

Look at Rugs-Direct.com for area rugs for your room. If you use a good photo of your space you can "try" the rug on your computer before you order one. See examples below.

A non skid backing indicates a very inexpensive throw rug at the WalMart, Costco price level. Even the rugs at HomeGoods and TJ Maxx typically don't have non skid backings.

Thank you all for your much needed advice- just WOW!

BeverlyFLA Deziner- thank you for the website :) the area rugs on that site are just what I was looking for and still affordable. Do I need to purchase a pad- premium or low profile for the bedroom since the king bed will be on top of it?

I am thinking the pad may be useful in the great room since there's more of the carpet that will be walked on.

Please note possible positions for area rugs under Queen or King size beds.

What is often recommended is a simple Felted Pad