when I visit the area, I don’t have the time to spare to do the whole thing so I miss out the east side of the North and just go straight to the more spectacular West. That said, I still think you should do it all, if only to see the controversial statue of the duke of Sutherland which stands 100ft tall atop an imposing mountain overlooking Golspie, really quite impressive.
I’d say do the east first and quick, save the best for last and I wouldn’t be too bothered with sticking only to the route they suggest, there are lots of equally spectacular roads there which aren’t on the route.
Can’t help you with places to stay, I only do bits at a time on day trips.