I had looked into driving the entire Ring Road but since we'll only be there October 3-9 I wasn't sure that'd be enough time to do it properly. I have no problem taking long trips out driving/hiking/etc. far from the city.
You can do the entire Circle in one day. The majority of the sights are DIRECTLY along the roadside, No need for hiking at all.
You CAN do the circle in more days if you want, but it might be a waste of time. .
So if you can schedule 1 day for the golden circle to get it out of the way.. Or incorporate stops from the golden circle into your other travels.
I would suggest do the whole thing.
Just look up a tour website and copy their itenerary, and drive the path yourself.