As per the OP's 3 calibers listed and as already mentioned, any of these calibers will do the job on large varmints or deer. I hunted deer with a .220 Swift 700 BDL Classic for 2 years using my chuck loads out of my other Heavy barrel Swift which used Nosler 55 BT's, shot 3 deer with that rifle and they all did not run at all, (neck or head shots). So you can't go wrong with any of these very cool calibers. As also mentioned, having total confidence in your shooting abilities, equipment, shot placement and hand loads goes a long way towards getting it done.
Frank
Frank