Either a .243 or a .270 would make a great choice. The .270 gives you a bit more power for larger game over the .243 but the .243 is easier to shoot in the long run thanks to its mild recoil. The .270 doesnt hit real hard either, but does hit a bit harder than the .243. For what you are doing though a 30-30 would probably make a real nice first gun for you since it will do everything that you stated as long as your shots are kept to 150 yards and under. Not to mention that they are easier to pack and are very mild to shoot and the ammo is cheap too.