If you have an AR already and you want to do it cheaply, you can buy a barrel chambered for .300 AAC Blackout and that's all you need. The .300 Blackout's parent case is a .223 Rem, so you can use your BCG, mag, etc with it, just need the barrel. The ballistics of the .300 are not the greatest, but it should down an elk if you are hunting under 100 yards.
The 6.8 SPC is a good caliber too.
But from what I know, the 6.5 Grendal is the best of the calibers in terms of long range, ballistics, and hunting. With the 6.8 and the 6.5, you will need another BCG for that caliber, mags, and barrel. I do believe that the 6.8 and 6.5 can be built off of a generic Multi caliber lower reciever. As well as the .300 BLK of course.
Hope this helps, good luck!