Hello Brewke,
The way I read your original post, you're making an Indy-Provo trip. My read of Midwest Michael's response indicates he sees Provo-Indy.
Assuming you're headed west and want to go to KC, I'd just stay on I-70 all the way through Denver, the Rockies, and into central Utah just past Green River. There US 6 takes you northwest to Spanish Fork, just south of Provo.
If the weather is looking bad in CO but good in NE, WY and northern UT, you can run up I-29 to NE-2, bypass Lincoln, thence join I-80 all the way into UT. If there is active bad weather entering UT, turn west on I-84 to Ogden rather keeping I-80 over Parleys Summit. It's a few miles farther but you avoid a +7,000' pass at Parleys.
I'd have a long look at the forecasts along I-70 and I-80 before leaving KC. If you're equipped, you can check the CO, WY, and UT webcams linked to their Dept of Transportation websites. All of the routes described herein have a number of webcams showing real-time road conditions, and they're usually at "trouble spots" like passes. That said, it's rare for a pass to be closed for more than a few hours.
Oh, and have a look at the "chain laws" for the states you're traveling through. You might be wise to purchase chains, and if you do, by all means practice putting them on in your driveway. The "chain up area" along I-80 in Wyoming is not the place to break the seal on the box.
Foy