Not suggesting these rugs, just using them to show round vs rectangle in there. I like the round best.

8’ round —

5x8 —

8x10 —

If you want to play around with mock-ups, eSaleRugs and RugsUSA both have that feature (as do other sites).

Envision the space and look at inspiration pictures using a round rug. Have you considered a square or rectangle instead? You could tape out to see the size required to protect floors and also create a nice balance in room in general. Consider complimenting rug in family room

Thanks for your help! I went with an 8' round rug