Any of the big 30's will do , 300 RUM, 30/378 , or the 338 Lapua, 338/378, etc.
The biggest problem for you is not the equipment but the time and effort invovled in using the gear at long range so you can kill out there with consistancy.
A top quality range finder is mandatory, and a set of swarovski big eyes are what my friends use.
Their rigs are mounted on transit tripods, and are the same 1000 yard bech rifles they use in competition.
They take deer out past 1,000 regularly.
there are some guys that shoot other stuff off bipods way out there, but they are face with the problem of being able to see as they are lower to the ground.
It works well if you are on slightly rolling prairie , however.
But , if you are looking for a competition rifle and not a bench gun or a hunting rifle a 308 will do fine, as will many of the different 6, 6.5, 7mm, and 30 cal cartridges out there......
Cat