I must admit to a north west bias but these are some of my thoughts...
I would consider doing the route anti clockwise i.e. north from Inverness up the A9 coast as you get better views especially travelling down the west.
North of Dingwall, take the B817 at Evanton and join the A949 which takes you up the heights with great views of the Cromarty and Dornoch Firths. Follow road to Bonar Bridge then east to re-join the A9. adds a wee bit to the journey but well worth it.
After leaving John O Groats travelling west on A836 to Betty Hill take detour to Dunnet Head which is the most northerly mainland point on the UK.
Travelling down west coast from Durness there is a x-boat memorial at Kylesku bridge car park along with some spectacular views.
South of Kylesku take to B869 single track coast road and meander through Drumbeg, Clashnessie, Clachtol, on the way to Lochinver (famous pie shop for those with deep pockets). From Lochinver you can take the main A837 to Ledmore then south to Ullapool on the A835 or take the road which starts up at the harbour end of the village to Inverkirkaig and on to Achiltibuie settlements a challenging single track road!!). There is a good loop route here which brings you back at the starting point and takes you past the Furan bar and campsite just past Polbain.
Heading east out of Ullapool on A835 for 12 miles then take the A832 road through Dunndonnel, Laide, Aultbea (WW2 gun emplacements and information), Poolewe, Gairloch to Kinlochewe. (worth popping up the single track roads heading west at Laide to Mellon Udrigle beach, at Poolewe to Cove (WW2 Russian convoy memorial). Follow road from Kinlochewe to Torridon, Sheildaig and the coastroad to Applecross then over to Lochcarron by the pass. On the way back to Inverness, a stop off at the Blue Ocean food wagon at Garve village hall is recommended.
Petrol- Petrol stations all reachable on the North and West coast roads BUT limited on Sunday. Tongue and Durness may be closed on Sundays but 24 hour fuel credit/debit cards) at Scourie , Applecross and Lochcarron (also I think at Gairloch). On the west there is fuel at Lochinver, Ullapool, the Dundonnel hotel, Laide post office,Gairloch and Kinlochewe.
Plenty of good campsites along the way e.g. Durness, Scourie, Ullapool, Polbain, Poolewe, Gairloch, Kinlochewe, Applecross.
B+Bs in Ullapool such as Ladysmith Guest House, Riverside. Good accommodation at the Arch Inn.
Anyway that's my bit. PM me if you want to pop in for a coffee in Ullapool.