As Buck said, I'd take I-90 to I-25, but I'd go through Denver and stay on I-25 to Raton NM, then take US-64 to US-87 to US-287 north of Amarillo.

CO-470 is a tollway with license plate tolling if you take it, no cash booths. I-25 through downtown Denver is okay except at rush hour. If you take 4 days, you will be going through Denver close to midday.