For getting out here in December, From Stockton I would take I80 to Salt Lake and then head south on I15. Catch 6 at exit 258 and drive down to Green River where you can take I70 west.
If the weather has been clear for a few days, you might chance I80 the whole way. The problem is that damn blowing snow can persist for days, even weeks on that pass East of Rawlins. Once you are over the pass, it's generally fine but that stretch just gets gnarly if you hit it at the wrong time.