Some things to consider in your quest:
Your terrain and distance of travel on foot is a consideration that you need to consider...If hilly with more than gradual inclines, weight and portability is a major concern..The AR platform is fairly light, but hard to carry comfortably if both hands are needed for stability for ascending or descending steep slopes...
Heavier 'varmint' type configurations get pretty old if having to travel very far between setups..but are great for longer distance shooting...If you are normally in brushy or timbered areas, the shorter configurations are much easier to maneuver for rapid, close up shots..
The AR platform is not for everyone, so if you get a chance to try one out before purchase, it will be best, especially if you have a long time history with a bolt action..
The .223 caliber provides a wide range of bullet/cartridge types and weights..The ammunition is generally easier to find under normal conditions if you don't reload...If you do reload, the components are generally available...Other calibers may be more spotty, depending on your specific locale...If most of your shots will be at 250 yards or more, then you might consider the .243 caliber as a first choice and a .204 as a second...The .243 will give you the benefit of a heavier bullet with more terminal energy...There is little ballistic difference in trajectory and energy between the .204 and the 22-250 at longer distances, but the .204 has less recoil allowing for easier observation of your hits...