You should base your route on which one, or rather which combination of routes, matches your interests and goals for the trip which you haven't mentioned. There is no one 'preferred' [best] route as the whole beauty of the road trip is getting to choose where you want to go.

If you want to see more of America than just City's, my preferred choice would be to create a route from LV to Chicago through the Four Corners region where you will find wonderful scenery and a high concentration of National Parks. From SF to Vegas a popular route would be to drive to Yosemite NP and cross the Sierra Nevada on the Tioga Pass [CA120] and down to Death Valley on 395. From Vegas the Grand canyon NP would be on most peoples itinerary and there are plenty of options to choose from in Southern Utah [Zion, Bryce canyon, Arches and Canyonlands] and Colorado [Colorado National Monument, Mesa Verde, Black Canyon, Rocky mountain NP] as well as some wonderful scenic drives and towns.

You won't be able to do it all so you will have to decide how much time you wish to spend at the destinations you have listed and how much time you have for the journey. You can then study a good map, research all the info here at RTA and see what appeals to you. Once you have the basics down, we can help to fill in the gaps, make suggestions and answer any further questions.

Enjoy the planning, it's a fun part of the journey !