If you really want the fewest curves possible, take newly opened US 34 from Estes Park to I-25 and Pueblo, and US 50 to Salida, then US 285 north to Buena Vista. Of course, that means you drive through the traffic of Denver, Colorado Springs, and Pueblo and probably adds 100 miles to the trip, but it gives you fewer curves.
I'm being facetious, of course, because it is impossible to see the mountains of Colorado without driving on roads with curves and grades. All of US 285 between the mountain front SW of Denver and Kenosha Pass is nothing but curves. So, yes, US 285 is your best route, just avoid it on Friday and Sunday afternoons when it is bumper-to-bumper. After Salida and the short grade over Poncha Pass, it is straight and nearly flat through the San Luis Valley all the way to Alamosa via US 285 to CO 17.
