Keep in mind the more magnification, the higher the scope will sit above the receiver. Then it may take a bit too long to find the crosshairs. For forty years my 30-06 wore a 3x Weaver and I could be on an animal in it in a split second. I moved up to a 3x9 Nikon a few years ago. Now I'm using "low" Warne QD (quick detach) rings that are slightly higher than the "medium" Weaver rings that were formerly on it. I notice the difference. In my opinion, for field hunting it's best not to have a real tight cheek weld to find the crosshairs ... or a real loose one. Just be on the gun comfortably without having to hunt for the crosshairs. This can be important if shooting long distance where parallax becomes an issue. A loose cheek weld can be a problem then. And a scrunched cheek weld can make fast shooting difficult. Go for the middle of the road.
Long distance shooting is for the experts. A lot of guys (like my brother) think because they have a magnum rifle with a fancy high power scope, they should be able to shoot animals in the next zip code. There's more to it than just the equipment!.
My 3x9 usually sits on 5x. I will turn it up at the range or to study an animal in the field. If I'm tracking something in heavy cover or close quarters, it's turned down to 3x or comes off and I pop up the iron sights.