AR build - 16 or 20 inch barrel?

Well, I've decided to build an AR. I'm pretty well set on how I want it to come together. I do have some questions about barrel length though. The rifle should be relatively light and easy to handle. I'd like to make head shots on the occasional deer inside of 250 yrds but it will mostly be used as a general purpose rifle. Long range beaver kills, home defense, plinking, and zombie apocalypse type situations. The military claims combat accuracy out to about 500 yrds with the carbine. Will the 16 inch barrel really provide me with the accuracy that I'm looking for or should I step up to a 20 inch barrel?