I have all three calibers,and like all of them. It would all come down to what caliber you deem having an advantage for you.
You can get a little more velocity out of the 25/06 with the same weight of bullet,but the barrel on the 25/06 will heat up faster than the other two calibers.
With the 6.5mm calibers,you can get some really great flying bullets,the only bullets that would come close in a 25/06 would be the Berger VLD's. My Savage 110 FLP 25/06 doesn't care for bullets under 100 grain,but my Custom 6.5 Creedmoor,and my DPMS LR-260 both shoot the lighter bullets well. I don't ever shoot factory ammo,so I don't know what types are easily found for any of these calibers.
Since you also want to target shoot,I'd go with one of the 6.5 mm calibers.