Winter basics for cross country trip.
Hi and Welcome to the Great American Roadtrip Forum.
The most important information you have not given us is 'how much time do you have for this trip'?
At more than 2600 miles via the most direct route, this is a solid five days trip - 4 overnight stops. And that is without sightseeing.
The best route for you will be the the most direct route which is going to give you the least chance of getting caught in a storm. So start watching the weather forecast in the days leading up to your departure, and see which interstate is most likely to have clear weather for the duration of your trip. Make sure you have an extra day, that should you get caught in a surprise storm, you can sit it out in a nice warm motel.
Drive safely
Lifey