If you contemplate shooting game at ranges approaching a half mile, you first have to have the rifle and load that will shoot MOA at that range, and that you can place within a half minute of your point of aim on demand. Using a suitable rifle, if you were to fire 10, 20, or 100 rounds at a paper target at any range, 80% of those rounds would fall well within 1 MOA. That means you should be able to consistently attain 80% hits on a clay bird at 800 yards if you can shoot up to your rifle. Therein lies the difference between intrinsic and practical accuracy at long range. Now if you were to go out each morning for a month, regardless of weather conditions provided you could see the 800 yard target, and fired 1 round, what would the group look like at the end of the month? If its larger than 8" you aren't ready. If it extends more than 4" from your point of aim, you aren't ready. If you can't carry out this drill for a month, you don't have the opportunity to get ready. I think you can see where this is headed.
The correct cartridge is the one that has the capacity for putting a high BC bullet on target with a minimum of 2000 fps remaining velocity. Most folks will agree that it takes a minimum of 1700 fps for a game bullet to reliably expand, but at 1700 fps, the degree of expansion is also minimal, although the resulting penetration will be pretty good. Impact velocities of 2000 fps have provided excellent performance in the game fields since the introduction of smokeless powder and jacketed bullets. Your cartridge should be able to put a heavy for caliber, high BC game bullet on target, with a remaining velocity of 2000 fps; a ballistics table will provide a pretty good idea of which cartridges are appropriate.
You can expect to spend upwards of $2K on a suitable scope for this sort of thing. Think in terms of S&B, Nightforce, and US Optics, supported with equally good mounts. Learning to correctly use a Horus style reticle has two major advantages over adjusting the scope for long range shooting. First its faster to adjust for windage and elevation by simply using an alternate aiming point within the reticle, and secondly, you don't need to be concerned about mechanical errors within the scope adjustments. A scope costing several thousand dollars should have reliable mechanical adjustments, yet we still hear of problems occurring, particularly as adjustments move out from the center of the adjustment range. If you're serious about long range shooting, and you have to choose between a $3K scope and a $5K rifle, buy the scope.
Next is the trick of acquiring appropriate ammunition. If you think you can simply follow the procedures outlined in your loading manual to attain suitable ammo, your first trip to the range will be an eye opener. Everything matters. Case capacities must be the same, neck hardness must be the same, necks must be concentric, powder charges must be the same, primer pockets and flash holes must be uniform and free of burrs, primers must be uniform, and bullet seating must uniform. Extreme velocity spread should approach single digit. If you can measure it, it matters, if you can't measure it, get better measuring tools.
Achieving these things is not impossible, but they do require dedication bordering on fanaticism, opportunity, and deep pockets to achieve.