Parallax adjustment will be necessary if you are going to higher magnifications. If this is a stand or bench rifle, then more mag the better. Will give you options if you need to thread the surroundings to your trophy.
However, depending on the size of game, high magnification is not always necessary. Scopes with good optics, a 10X is very useable on large game at long range.
This is how I have set up my hunting rifles. My walk about '06 uses a B&L 4000 in 2.5X10 with turrents. Gives me the field of view for "normal" hunting ranges and the 10X for long range stuff. Personally limiting this rig to 700yds, however the optics are capable of putting the cross hairs on a deer at 1000yds.
I have a 30 Gibbs that is still portable but mostly for clear cuts and some LR pokes from the truck. This wears a B&L 6X24 with turrents and will go as far as I can range with my Leica 800( about 950yds).
I would suggest against a scope that needs an AO if you are planning on still hunting with it. I have missed game when the scope was put on too high a mag and forgotten or the image was out of focus. For my still hunting rifles, simple is best.
Leupolds have a strong following on this board. Other worthy scopes are Baush&Lomb Elites, Nikon, IOR/Valdada, Tasco Super Sniper, and even some Russian stuff.
Always look through your scopes before buying. You will find that some brands just don't look right. For me, this is several Leupold models. My eyes seem to like Japanese glass better.
A scope is more important then the rifle. You can't hit what you can't see. You can always adjust your aim.
Jerry