How to legally carry a firearm in your vehicle while traveling across the country?

My wife and I are taking a road trip to my wife s hometown in Colorado, leaving from our house outside Washington, D.C. In Virginia, in our little Honda Accord. As I have spent my whole life living in the city, I don t often have the opportunity to do any shooting and am considering bringing a firearm along.
I have a 9mm German Luger P08 1937, a Browning Light-Twelve semi-auto 12 gauge shotgun, and a M1903 Springfield 30 06 Rifle.
As all three of these guns are WWII era or earlier I don t have any papers or proof of ownership of any of them. I am over 21 and have a clean criminal record, but I don t have any kind of permits either.
We will be traveling through Virginia, W. Virginia, Kentucky, Indiana, Illinois, Missouri, Kansas, and Colorado, but also possibly Nebraska, Iowa, and/or Ohio.
I don t imagine there is any legal way for me to bring the Luger, but is there any way to legally carry either my shotgun or rifle in my vehicle? And if so, is there any states that I should avoid and plan a route that doesn t take me through any states that it would be illegal?
I would greatly appreciate any information that would help me to come to a conclusion, as we will be leaving in about 14 hours. Thank you!

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