When you consider cost, just about all bullets and brass 30 cal and below cost the same. Barrel life, slower is better, but you need fast to get to a mile and beyond. I think you'll just have to deal with shorter barrel life. But consider, even 'short' barrel life is around 2,000 rounds, and you will spend much more in 2000 rounds of ammo than you will on a new barrel. Also, to get to those ranges, you need a heavy, slippery bullet. Those are expensive. JLK, Berger VLDs, and Lapua Scenars are what you'll be shooting, and the bullets alone cost more than a hand-loaded 308 Win with Hornady AMAXs.
What I'm trying to say is that distance costs money. You can do some things to cut cost, but in the end, you're gonna need an expensive scope, an expensive rifle, and expensive ammo.
I've only shot at 1000 yards, but even when I did my best to cut cost, I still had a $2500 rifle in the end.
Sound barrier is where bullets get funky. There's only maybe 50-100 yards more of usable accuracy once the bullet goes below the speed of sound because of the 'kick' in that transonic zone. A mile is 1600 yards or so.
300 Win Mag / 300 WSM / 300 RUM- Advantages: tremendous ballistics. Disadvantages, shorter barrel life. Sound Barrier at 1700 yards
7mm Rem Mag - Advantages: Lower recoil, good ballistics. Disadvantages, even shorter barrel life, Sound barrier at 1600 yards.
6.5x284 - Advantages: even lower recoil, popular for competitions. Disadvantages, still a shorter barrel life. Sound Barrier at 1600 yards
6.5 Creedmoore - Advantages: common components, lower recoil, popular with tactical shooters, box ammo. Long barrel life Disadvantages: inferior ballistics to the magnums. Sound Barrier at 1400 yards.
308 Winchester - Advantages: very cheap ammo, low recoil, easy to reload, can buy components in a store. Disadvantages: Runs out of steam much sooner than more modern cartridges. Sound Barrier at 1100 yards.
In comparison, 338 LM - Advantages: Amazing ballistics. Disadvantages: High recoil. Very expensive ammo, even for reloaders. Limited rifle choices. Short barrel life. Sound barrier at 1750 yards realistically, claimed 1950 yards with Berger Hybrid OTMs.
50 BMG - you know all the advantages and disadvantages. Sound barrier at 2550 yards.