RE: .243 Win, 6mm Rem, .240 Wby?
I would choose the 243 Winchester hands down. If you want a only varmint cartridge then I would choose a 22-250 Remington. One time I was hunting with my Ruger M77 MKII in 270 Winchester and I suffered a mechanical failure. Just so happens I brought my 243 Winchester along to hunt coyotes after my deer hunt. I brought 2 kinds of reloads with me, Hornady 75 grain v-max and Nosler 100 grain partition. The 243 Winchester saved the day.
I also went on an Antelope hunt to Wyoming and only brought my 243 Winchester with only one type reloads. The night before opening season my friends and I decided to go varmint hunting, so I used the only ammo I brought. I shot a big male coyote at 50 yards with my 243 Winchester using Nosler 100 grain partition. The owner of that sheep ranch shook my hand and said I saved him 10 lambs this spring.