The bolt face will have to be opened up from .473 of the .25-06 to .532 for the .264WM. Unless you're dead set on the .264, I would make it a
6.5-06, 6.5 Sherman, or 6.5-284, it would be a lot simpler. The .264 will
push 140s at 3200fps and the 6.5-06 and 6.5-284 will give you 2950-3000. The Sherman is right with the .264 on velocity but is based on the .270 Winchester and you don't have to mess with the bolt face. The easiest option is the 6.5-284, no fireforming, no custom dies, no custom reamer, and you don't need to change a thing other than the barrel.
As far as barrels go, I'm not a big fan of the look of carbon fiber, but they offer heavier barrel contours than steel while being lighter. So you can have a varmint contour carbon wrapped barrel and it weigh the same or even less than a sporter barrel made of steel. Carbon barrels cost double that of a match grade stainless barrel though. The best Carbon wrapped barrels are made by Proof Research. They are cut rifled and from the reports I have seen, they shoot just as good as any. There are others who make carbon barrels, but none have the reputation of Proof.
For stainless barrels there's a lot of options. Cut rifled barrels are considered the best and people will argue forever about Cut vs. Button rifled barrels. The fact is, they all shoot well if you get a good one. Some of the best cut rifled barrels are Bartlein, Krieger, Brux, and Hawk Hill. And the best button rifled barrels come from Hart, Broughton, Benchmark, and Lilja. I'm sure I'm forgetting some, but those are the ones you'll most often see and hear about. Just find one of these barrels in stock that is the caliber, twist, contour, and length you want and order it. Don't overthink it, buy a good one once and it will pay off.