RE: Texas Hunting Rifle
I own a .243, a 7mm-08, a .308 , and a .270. There is not much difference between the 7mm-08 and the .308. They are a little bit easier than the .270. In my opinion, if you want a light recoiling round that will still work for you than get the .243. You can also get a good recoil pad installed on it if it does not come with a good one ( based on the gun you choose ), and you can get a shooting shirt with a pad onthe shoulder. With this combination, you should be able to shoot just about all you want to.
If you did desire a larger caliber, you can move up to the .308 and buy some remington managed recoil ammo or some federal low recoil ammo. and shoot that. This ammo uses a faster expanding bullet ( at lower velocities ) and a lower powder charge, to get the lighter recoil. The recoil isslightly less than a standard.243 round, and has the energy to make it effective on game out to just over 200 yards. I have tried both brands, and it does what the companies say it does, and is a quality ammo.
Remington Managed Recoil is available in( .270, 30-30, 30-06, .308, ) less recoil than a.243 --- (.300 mag, and 7mm mag. ) more recoil than a .243.
Note: Managed recoil ammo will not cycle a semi-automatic rifle fully, to eject the spent case.
I hope this helps.
Good luck and God bless.