Now days there are numerous calibers to choose from.If you plan on shooting 200 and 300 yards and nothing more,then you will suffice with a 223,222,221 Fireball,if you plan on learning to shoot at some distance then the 223 is still a very good option to start with,but ONLY with a 55 grain bullet,WHY? Simply because the Bal.Coefficient is greater in the 55 gr than the 50 or 45 gr.Bigger Bal Coefficient means better down range flight and best all around shooting for longer range.
Now you would be a lot better off caring 2 or 3 rifles if you have them so you can be soaking one rifle while shooting another one,but if not carry what you have,but LEARN to shoot long distance!! It can be done without trouble.Lets say go with a 223,22~250 or Even 220 Swift,,<~~That's MY FAVORITE,BAR NONE) 243 with a 70 grain bullet KILLS the hell out of Coyotes,Prairie dog,and everything in between.That's the bullet to shoot in 243!!! BAR NONE!! .In the 220 Swift the 55 grain for regular shooting an the 60 grain for wind.Its a DYNAMIC KILLER!!!! It is totally unforgiving for fact.