One thing that you should consider is your accuracy. I'm not talking about the accuracy of the ammo or of the rifle, but of YOU. You need to determine what groups you can consistently print at various ranges shooting from hunting positions. To do so requires a great deal of practice. Some excellent practice routines involve over 50 rounds a practice session, printing numerous 5-shot groups repeatedly from various positions. This translates to some serious amounts of ammo. If you stick with factory ammo (as many newbies do) then the 223 is a more sensible choice. It is a proven coyote dispatcher and can consume very inexpensive practice ammo. Even some perfectly adequate hunting ammo in this caliber is cheap enough for high-volume practice.
However, if you get into handloading, the 204 can be cheap to shoot as well.
Just something to think about
