Thanks for the better explanation, it makes answering easier for me
I would choose the .243 Winchester for what you're wanting. Ammo is reasonably priced and available (at least around here), recoil is nothing, and it is considered an inherently accurate round. The .308 would be a great choice but it does recoil more than the .243 and that can mean something after a full day at the range. I don't think any of the choices you list are bad and would not hesitate to use any of them for your stated purpose.