While the 25-06 and the .270 are my personal favorites here, I would take the .243. As your first centerfire rifle, it's more important that you can shoot the rifle, a LOT, to get familiar with firing it. Start with some reactive targets, like steel plates, and graduate to paper targets. Do your best to keep your eye(s) open and watch the reaction of the target. That takes your mind off the recoil and makes you concentrate on shooting the rifle, rather than trying to survive the recoil (which won't be much, believe me).
Disclaimer: I've never fired a .243, but I've fired a 22-250 (essentially the same with a lighter bullet), and the recoil of those could be described as "non-existent".
Disclaimer: I've never fired a .243, but I've fired a 22-250 (essentially the same with a lighter bullet), and the recoil of those could be described as "non-existent".