5.56mm is adequate for deer @ 300 yards and in. As long as you do your part, the rifle+bullet will do their part. I would recommend 75grain Vmax bullets.
Think about it this way: Even with a .50BMG, there is no guarantee of a DRT shot. Go on youtube.com, type in .50BMG hunting, click search. There is a video of a hunter shooting a doe at about 200 yards with this caliber...go ahead, look it up- I'll wait...okay, did you see that? Well placed shot, well
within the capability of the weapon and the doe still ran off about 50 yards
. When the hunter walks up to it, you see the devastating exit wound the animal had (about a foot across) and you saw it run didn't you? You know what this tells me? No matter how much gun we use, the desire for an animal to live can greatly overshadow the power of any
Do you know what else that video tells me? That anything
less than the .50BMG round cannot guarantee a DRT.
With all that said, do people mean to tell me that @300 yards the 5.56mm round has less
power than an arrow from a bow @20 yards? I doubt it.
Besides all that, I would recommend you stick with something easily available to shoot in your area. Personally, I reload my own ammunition but I try to load something similar to match grade factory ammo.