270 WSM is a good choice recoil is that of a 30-06 easy climb I have a Winchester Model 70 that is very accurate and reliable a 243 is also a great choice.
30-30 with a good scope should be good after all if it was good enough for our great and great great grand pappy's it 's good enough for us in addition the 223 and 7mm08 Remington would be great for speed goats.
You could keep it in 25-06 but improve on it such as replacing the magazine with one that accepts detachable magazines improve the accuracy buy installing new sights and or scope and maybe replace the bolt.