FIRST, develop a list of calibers that keep above the 1000 foot pound threshold at 300m. It's an arguable criteria, but something has to be used. That means that most of the calibers above 6mm moving at least 2,500 to 3,000 fps will retain 1000 footpounds out to 300m if they have at least a .300 BC.
Then take that list and apply it to the list of available calibers in the AR10/15 and you'll find most are a match, and it will be available for less than $1000. The interesting part is that a simple 2MOA milspec barrel will do it - that's a six inch circle on a target with a lethal hit zone about 18 to 21" at 300m.
If you trend toward the smaller calibers, look for higher speeds in ammo to retain the 1000 footpounds at 300m. They will shoot flatter and require less drop compensation or practice to learn.
The limiting factor will likely be figuring out which of 25 or 30 cartridges would work.
Why the AR? Better controls for operating it, lighter weight, easy to mount an optic using an A3 flattop. That doesn't work for the older .308 military rifles, and are much of why they were pulled from service - something better came along, just as they replaced older designs.