If this is a high volume Varmint rifle, and weight isn't a big deal. I would get the heaviest barrel you feel comfortable with. Fluting wouldn't be something I would do if weight wasn't an issue. I also wouldn't be putting a carbon wrapped barrel on a high volume rifle.
There's a lot of good barrels out there right now. I prefer Bartleins, but Krieger, Brux, Hart, Benchmark, Broughton, Lilja, and a few others are all premier top tier barrel makers. Find one in the contour and twist you want and buy what's in stock. Don't get too caught up in brand. When you find a maker that works for you, then you can choose to stick with them for your next project, or try another top barrel manufacture.