We did come back from Denver to Dallas via Salina, Kansas and Oklahoma City, but that was to try to outrun a snow storm on a skiing trip. It is Interstate all the way: I-70 to I-35. That is the only time we have ever followed that route and it would not be my choice, but the highways were all Interstate.
There are three alternate routes but they all go through Amarillo. The one we usually take is US 287 from Wichita Falls to Amarillo, then through Dumas and Dalhart to Clayton, NM and then on to Raton where we pick up I-25 north. That is still our route of preference.
Alternate number two is to stay on US 287 to Limon, Colorado through the Oklahoma panhandle. I've only been on this route on a church bus on a ski trip.
Alternate number three is to cut across to College Station and Temple on the way to Lubbock, then up to Amarillo where you would have the same two choices above. If I were coming from Houston (especially from the north or northwest part of Houston) I might consider this as a "non Interstate" route. I have not followed this path as I do not live in Houston, but I often take state routes and US highways to avoid large cities.
Anyway, these are just some thoughts on the routes from Houston to Denver.
We have never stayed in an RV park around Denver. Many times in Colorado Springs and in Estes Park. -- not to mention all over the state of Colorado.