I've made the drive several times when I was stationed at Nellis and later once I moved to Boise. I would say taking I-93 and then take Route 6 out of Ely to Route 318 and you'll pick up 93 just south of Hiko. 318 runs paralell to 93 and it will cut a good deal of time off your trip.
One of my friends swears by taking I-15 through Utah when driving back and forth from Boise/Vegas, but if you want to take your time and enjoy yourself go for it.
I always made sure I had extra provisions and plenty of CD's. Its a long boring drive and one I'll not take again. The one thing I was always worried about was breaking down because you would be screwed. Thats why I always had my ruck filled with MRE's and survival gear in case help didn't come along too soon. My wife and I often felt like the last people on Earth when making that trip. I can remember driving for 3 hours without seeing another car. My wife made that drive a few times herself in a used Ford Escort.
Good luck and have fun at your school.