AFAIK it's much easier to make a very accurate rifle with push feed. All the bolt has to be is flat on the face, tight and consistent when locked, perpendicular to the chamber face, and headspaced right.
Now this isn't as easy as it sounds, hence the price of a REALLY accurate long range rifle. Still, the CRF has more to booger up the accuracy.
This is no big deal in a hunting rifle. Getting 1 MOA with CRF is not a problem.
Bottom line? A good CRF is a far better feeding system -- but you probably don't need the best feeding system, especially at the cost of ultimate accuracy. PF is a better shooting platform for extreme accuracy, or for a relatively inexpensive rifle that is plenty accurate for practical use.
I'm not a CRF snob; my primary hunting rifle is a PR, and I don't own a CRF rifle other than milsurp.
(I do covet a new M70 Featherweight, but CRF is only a very tiny part of that equation. Fit, weight, balance and handling come first.)
Apart from tree stand use, dangerous game, and military applications that have been obsolete for the better part of a century, a PF will serve you fine. For what you want, it will serve you better.