I'd put a new barrel on it from the get-go.
1. I don't think it takes but a few hundred rounds to get proficient enough to shoot to the limits of a factory barrel (with proper instruction and dry-fire practice) What's that to a 308 barrel?
2. Once you get to the limits of your barrel, you're left wondering "was that me or the gun" more and more the longer you go with that factory barrel
3. It has been my experience that precision degrades the farther you shoot a factory barrel. 3/4 MOA at 100yd, quickly becomes 1-1.5 MOA at 800.
4. You MIGHT get around 1/2-3/4 MOA out of the factory tube after exhaustive reload testing. You can just about bet on 1/4 MOA from a new bartlein,brux,krieger, etc..
I can shoot my custom build (granted, it's a .260) out to 1300yd and my vertical spread is about the thickness of my reticle. Wind call errors can be immediately noted very precisely. And elevation data is usually spot-on, but if it's not, I can make that correction after 1 shot, not a 3-5 round pattern.
Guess which barrel I've learned more from-- my 3/4 MOA factory tube or my 1/4 MOA Bartlein.