Although it would be nice, it's hard to get a cartridge that is suitable for target/sniping to 1,000yds and also be capable of cleanly taking deer sized game at 1,000yds. I know everyone will say the military uses the 308 to shoot at humans at long range, but that's a whole different ball game than trying to cleanly take a game animal which is of much tougher construction.
Basically, the rounds that are capable of clean game kills at 1,000yds aren't suited to target/sniping due to short barrel life and excessive recoil. On the other hand, the rounds that are suitable for target/sniping don't have the required power for consistently effective results on game at long range.
Picking a hunting round is the easy part. Most modern cartridges can be accurate enough, as the majority of the raw accuracy requirement is up to the rifle it's fired from. So, any cartridge which provides enough power for the game is good enough. In today's world of extremely large magnums, there are several which are capable of taking whitetail at 1,000yds. However, the number of rifles capable of the required accuracy is much fewer, and the number of shooters capable of it is probably only a small fraction of 1%.
Now, for target/sniping, the choice becomes more problematic, especially if it will be used for competition where every available point can make a difference. Since barrel life and recoil are a concern, most of the magnums are out of the question unless you're dedicated to shooting 1,000yd BR. Again though, there are several good choices and a lot of cartridges can be made to work with proper loads and bullets. The 308 is a great example. It certainly isn't the ideal choice for 1,000yd shooting, but it can be made to work okay with proper bullet and load selection. Heck, even the 223 has been made to do okay at 1,000yds with very specialized heavy VLD bullets in fast twist barrels. Right now, probably the best all-around choice for accurate 1,000yd target shooting with low recoil and reasonable barrel life is the 6mm BR. However, other very suitable choices are the 260, 6.5x55, 6.5-284 (barrel life is a concern) 30-06 (recoil is a concern with 190s), 7mm-08, 308 and probably a bunch more that I can't think of right off the top of my head. Lately, I've been thinking about rebarreling one of my Savages to a fast twist 7mm-08 as it seems to me to be a great choice for long range that gets overlooked more often than not.
As for the rifle itself, a bolt action is of course the most suitable choice, because they're easy to make accurate, they're reliable as a claw hammer, and fast repeat shots aren't going to be needed at 1,000yds because it takes over a second for the bullet to get there and you almost certainly won't see where it hit unless you stir up some dust or hit a reactive target. So, unless you're absolutely certain you've made the correct elevation and windage corrections, you aren't going to be able to do any rapid fire. For somewhere between 1 and 2 seconds you're stuck waiting to see what happens to the target or get the call from the spotter. Rapid fire simply isn't practical for the application at hand.
Now, if I was going to use a semi-auto, the AR-15 or AR-10 is about the only rifles I'd choose, at least in a practical price range that the average person could afford anyway. I've never been able to get acceptable accuracy (for LR purposes) out of the other common "hunting" semi-autos. In my experience, the BARs aren't good for any better than 1 MOA, and that's if you happen to get lucky and find a good load. The 7400s I've shot weren't good for any better than 1.5" even with good loads. Now, before someone says theirs shoots better than that, well yeah anything is possible, but I'm talking about always shooting MOA or better. Although wind reading ability and having low SD are two of the most important factors for LR shooting, and your short range groups often don't correlate to the LR performance of your rifle, if your rifle won't always hold MOA or better at reasonably short distances, then you're probably going to be very unhappy when you shoot to 1,000yds.
