I wanted the same type of barrel a few years ago on a model 70 22-250 sporter I shot out. I went with a number 3 contour Krieger barrel. I also have a couple of Tikka sporters also. I think they would be more like a number 2 contour.
For a rifle that get carried a lot walking I think the 3 is a good compromise. Personally I wouldn't want any larger. Kind of depends how the rest of the rifle is set up. What stock, scope weight, bipod on or off?