The way to get good at long range shooting is by long range shooting. You'll quickly discover that 500 yards is just the start of long range. It takes a solid investment in time, money, and perseverance to reach a level of competence.
That is not to say that you need to spend a fortune on your rifle, I started long range shooting with M-17 Enfield in .30/06 with a 3-9X Bushnell scope. Essentially the .308 and the .30/06 are ballistically identical with bullet weights below 180 grs, but you can't skimp on your ammo. Factory match is stupid expensive, I shot factory Lapua match for a while, so believe me when I say you must handload. Anyway, with my surplus rifle and cheap scope, it wasn't long before I was ringing steel over 800 yards away, and knocking the plates down just often enough to encourage me to get a real target rifle and a more suitable scope. I badly wanted to be able to dial in the range and hold dead on, rather than setting up an aiming target high above my impact target. Due to the modifications I had to make to the rifle due to misaligned mounting holes, shimming the base was not possible.
I went through a number of .308s; a Mauser with a long heavy Sportco barrel, a Tikka Continental, and a couple of 700s, but for one reason or another, they didn't quite do it, so finally I invested in a custom rifle. From the Bushnell hunting scope on the Enfield, I progressed to a 12X Leupold then to a 6.5-20X. From the Leupold's I took a step down in magnification and tried an old steel 6X Khales sniper with a cam that matched the trajectory of a 168 gr MK at 2600. This scope allowed me to dial in out to 600+ and I still have that scope. From the Khales I tried a Springfield Professional 6.5-20X56, a really big scope that allowed me to finally dial in the range I wanted, but more importantly, taught me how big an impact even slight canting can have on group size at long range. The Springfield has a bubble level at the bottom of the reticle. But I still wasn't happy, as the preciseness of the Springfield's adjustments weren't consistent, so I finally upgraded to a S&B PM II. Now when I adjust 1 CM, I get a true value on the target, and I get all of the elevation adjustment in a single turn of the turret. Where I could walk my rounds onto the 12" steel plates with the '06, resulting in more grazing hits that knock downs, I could now make cold bore dead center hits on clay birds. When the range is too great to hold dead on with the scope adjusted for maximum range, I have 4 mildots below the reticle center that provide an additional 14.4 MOA.
Now due to the fact that this is the hunting and sporting arms section rather than the precision rifle section, I assume you intend to shoot game at long range. If that is your intention, your first step is to learn long range marksmanship. The second step must be to select a rifle that has greater down range performance; as a game cartridge the .308 is about out of steam at a quarter mile. A .300 magnum isn't a bad cartridge, but one of the big case .338s is better, but not better to learn with, so for now stick with your .308.
