I would guess leaving after Christmas you are looking to get there rather quickly rather than moving along slowly and sightseeing along the way, particularly considering weather uncertainties that time of year. If so, I would keep it simple and easy and just take I-35 to OKC or I-49/I-44 to OKC. Then I-35 to San Antonio And I-37 on down. You would have some toll road, about $25 worth, in Kansas or Oklahoma depending on route. You would have a few miles of construction in north Ft Worth, do that mid day and probably little problem. About 30 miles of construction between Waco and Salado, but generally not a problem barring an accident. Then you can either tolerate the traffic thru Austin, or take the bypass toll road at Georgetown to I-10 and skip it altogether.
There are numerous slower, more rural, more scenic routes on smaller highways and thru many small towns that many people prefer if they are in no particular hurry.
Haven't stayed at any RV parks on the route so can't make any recommendations.
