There are, generally, two types of 1000 yard rifles. Light Gun, and Heavy Gun.
Light Gun is really pretty close to a regular Benchrest Rifle. It has a 17 lb weight limit, which really does limit the design.
Heavy Gun has no weight limit. As long as the rest is two piece, anything pretty much goes.
I built a Light Gun last year, based on a Shehane Tracker Stock and a Bat M Action. It's a switch barrel, one in 6BR, the other 284. It's pretty standard stuff, sort of a scaled up HV in calibers suitable for 600 to 1000 yards.