Aww comeon we mention almost all the standard 06' wildcats but no 6.5-06?
My 3 top choices (in no particular order) are
- .270 win/ 6.8-06
-.280 rem/ 7mm-06
-6.5-06
They all perform roughly the same, and the differences mainly come down to when you start splitting hairs. IMO the .270 would be the most useful choice. .280 is a tad more efficient because of the larger bore diameter, it's less overbore, and slightly more efficient burning powder, but at the same time, has a caliber disadvantage over .277 so you need heavier bullets to achieve similar sectional densities and ballistic coefficients. IMO the .280 only has an advantage with the heaviest for caliber bullets, like 170-180 grains, but if you're re-barreling anyway, you could get a custom twist .277 barrel and shoot bullets like the matrix 175 grain VLD, which has an advantage over a 175 grain .284 cal bullet.
6.5 is a good choice because it has lots of efficient choices in the 120-140 grain range but of the three I listed will have the worse barrel life, and lowest raw muzzle energy, of the 3.
If you don't have reloading supplies, .270 gets another advantage with factory ammo. Factory ammo is made for the .280 but because it's less popular than other 06 variants, it can potentially be more expensive, also due to the early semi autos not being able to handle hot loads, the .280 has a lower SAAMI spec pressure than the .270 and most factory ammo is loaded milder for this reason.