I am new to hunting and am looking at various options. I am considering doing some hunting for mule deer in Montana. But I am unsure of an appropriate caliber for them. To increase my shooting skills, I practice with an AR-15 in 223 but I have a feeling that this caliber is not good for mule deer. What calibers should I be looking at?
In theory you could hunt Mule Deer with .223. I had friends who hunt boar with .223 and mule dear aren't really any tougher than a boar. That being said, smaller caliber equals less expansion and kinetic force. That means you have to be more precise.
If you are new to hunting, I would go with the classic .30-06. Good range, good ballistics, great range of available rounds/loads. You can hunt just about any large game in North America with one. It's a great first rifle for someone getting into large game hunting.
.30 cal is about where big game hunting starts. You could get away with .223 with smaller white tail deer, but you'll increase how often you need to track your deer and that's less humane.
For mule deer, I would stick to .30 or higher. I prefer Springfield 30-06, but that's just my preference. You could really use any .30 or higher.
My deer rifle is a .270. That is a smaller caliber than what either of the two current answers recommend. My father frequently carries only his .44 magnum bear pistol when hunting bear and/or deer. With my .270 I don't consider shooting bears, and he only considers relatively close shots.
In my opinion there are many firearms that can do the job effectively and humanely (ever wonder why "buck shot" is called "buck shot"). What it really boils down to is what firearms you have, your skill level with those firearms, and the type of hunting you want to do. Obviously these aren't factors that we can evaluate for you.
I agree with both current answers that the 30-06 is a solid firearm for your stated needs. If you don't have one, and you're looking to buy a hunting rifle, that is a great general purpose setup that I would certainly be comfortable recommending. Keep in mind that the real limiting factor is your ability, your comfort, and your understanding of your weapon's limitations. That is always true, and doubly so when engaging a target with deadly intent.
You don't need a .30 cal. to take Mule Deer. However they are a proven round, and I personally think they are a little easier to clean than smaller bores.
It's generally accepted that a .243 Win is a good starting point. And for the difference in recoil. You'll probably get much better at shooting starting off with that .243 which is more mild in recoil. .243 is also considered by most to be the smallest cartridge to consider for taking Black Bears as well. Though there are folks who actually take Black Bears with .223 Rem. yeah, crazy, I know.
I personally started off with a .308 Win. And it handles them with authority, given that you've done your job and placed the bullet properly. They do kick pretty darn good though. I have a prior collarbone injury and shoulder injury, so the buttstock doesn't lay flat against my shoulder when I'm prone, so when practicing after about 40 shots it starts to hurt pretty good and I have to tap-out.
For perspective, I'm relatively new to Hunting. At 45yo in 2014 got the notion in my head I wanted to do it and I wasn't getting any younger, so I'd better get with it. So far I've taken two Mule Deer hunting solo (2015, 2016) about 5 miles in from the vehicle. The 1st buck was with a .308 Win @40yds.
In the .308 Win the Barnes TTSX 168gr bullets worked amazingly well! That first buck got knocked like 10 inches sideways when I hit him at 40yds. A little high and back for a lung shot, but I think part of the energy got him in the spine as well. He pretty much dropped where he was. His front legs kicked for a little bit after, but not his back legs, so I think the spine sustained damage.
The 2nd buck I decided to take with my Marlin .30-30 Win because I hadn't taken game with it yet, and the terrain is brushy/chapparal and the shots are only like 40yds anyway. The shot placement was different on the 2nd one. He was moving and Quartering away quite a bit. The bullet entered at the midline of the body and took out the liver and the opposite side lung. The bullet didn't pass-thru on that one because it got trapped-in behind the scapula. Also the bullet path was probably a good 18 inches total. There was a little bit of tracking. And since it didn't exit, no blood trail. He ran maybe 35yds, but he was hard to see because one side of his antlers was missing. And he blended in soo well with where he dove under a bush.
The .30-30 Win is a pleasure to shoot compared to the .308 Win. In the .30-30 Win I used the Federal Premium Trophy Copper 150gr. The bullet retained all of its weight and mushroomed textbook fashion.
I bothered to share these two stories if only to note that you should also consider the terrain you will be hunting in. No sense in buying something like a .300 Win Mag if the terrain you're hunting in will never afford you those long distance shots anyway.
If I had it to do over again, I'd probably buy a .243 Win and it would be my everything gun. Varmint loads for coyotes, deer loads for deer/bear.
And oh yeah... if you have to back-pack and hike-in a few miles to your area... get yourself a model with a synthetic stock. You'll end up falling and scratching the darn thing out in the field, I gaurantee it, and the weight savings you'll come to appreciate in no time flat.
Also... don't go cheap on your hunting pack. You need one that can COMFORTABLY carry that weight for quite a ways.
Good Luck. Now go put in the required work!