Five years ago we took SR 58 out of Eugene to US 97 south to Klamath Falls. At this point we took SR 139 to Alturas, CA to take care of some DMV business. With DMV taken care of, we went north on US 395 to just north of Lakeview, Oregon and then SR 140 to US 95 and south to Winnemuca.
From what I recall, SR 58 is a delightful drive with easy grades. I have no info about SR 140 between Klamath Falls and Lakeview because of our Alturas detour. SR 140 from north of Lakeview to US 95 is a good 2-lane but very few services of any kind. There was one steep eastbound uphill grade of a couple miles. I strongly recommend that you top off your fuel in Lakeview before taking this little used ranch country highway.
Have fun. Drive safely.