Welcome to RTA, glad you found us!
I-80 is going to be your shortest and safest bet. Going further south to avoid weather is a fallacy. All of the routes have their downsides, like they'll add a day to your travel time. The best thing you can do is try to get an extra day "just in case" you have to hole up somewhere and wait out the weather. Chances are you'll be fine and won't need that day, but you'll want that extra day for peace of mind.
For your own safety, I would plan to use ALL 5 of those days to travel. You will have to travel 500-550 miles per day. In a smaller, 12-ft truck, this is do-able, but bear in mind you will be on the road between 10 and 12 hours per day. Stop every couple of hours to stretch your legs -- you will have to stop a lot anyway, to fill that truck up with fuel -- do some exercises, clear your mind. Treat it like a marathon, not a sprint. Stop and get food along the way.
I-80 will cost you in terms of tolls. I'm sure others here will offer some suggestions that would not take you far off your beaten path but allow you to get off the toll roads and onto FREEways.
As far as weather is concerned, none of us have a crystal ball. Keep an eye on the weather, using your smart phone, the TV in the motel at night, even TV's at the truck stops are often tuned to the weather stations. If the freeway gets closed, it will be your clue to get off and hole it up in a nice motel.
Donna