A wide variety of calibers have been successfully used for shooting accurately to 1000. .223 up.
A scope with clear optics and reliable repeatable adjustments is needed. Parallax adjustment is worthwhile. Even something like a vintage Weaver T-16 would be acceptable.
An accurate rifle is essential, and needs to be one that will shoot the bullets that perform at long range. A good used rifle can be a better buy than a new economy piece.
The cost of match grade ammunition will bring tears to your eyes if you do much shooting. The performance is there, but so is the cost. If you are going to do a lot of shooting, you'll need to handload, unless you are suffering from lower back pain because of the thickness of your wallet. Cheapest match grade ammunition I ever purchased was Hornady 155gr .308 Match at the DCRA matches @$30 a box. Buck and a half a shot. Can't get it for that now.
You will need the various accessories, of course. Once again, good used equipment can be cost effective. I was just viewing the promotion for the latest version of the Ckye pod bipod. Impressive and perhaps several times the cost of a bipod that would work just fine for someone starting out.