Howdy and welcome to the forums!

I myself use .223 and 25-06. I tend to use the .223 most of the time. It has almost no recoil, it is cheap and easy to reload for, and it has been accurate with almost every type of ammo I've feed it. For targets and coyotes, it is hard to beat. With 40 and 50 grain V-Max bullets, it won't even make an exit wound in most coyotes. The 25-06 has a little more recoil for target shooting, but wind drift doesn't factor in as much with the larger bullets. I shoot bullets ranging from 75-120 grains. It also packs a lot harder punch for distant critters. Although it does sometimes make for a large exit wound. The .243 rates somewhere in the middle. It is also flat shooting, just pushing bullets around 55-95 grains at about the same tragectory. For the purposes you mentioned, the .243 would probably suit you well.

With the improved metal used in gun barrels, barrel life shouldn't be a big concern.