Don't know what you mean by distance shots . . . or what you intend. Most deer, even here in the Rockies are shot at less than a hundred yards . . . certainly less than 200 yards. I think you need to be careful about approaching this subject . . . and you need to practice practice practice . . . until you KNOW you can do what you want to do. Some guys think that because they own a long-distance "Louden-Boomer" they are suddenly "long-distance shooters."
Well, enough preaching . . . on to the rifles . . . I think the 7mm Remington Magnum may be your best choice . . . although you can't sneeze at the .30-06 or .270 . . . assuming deer or antelope is your game. A .270 or 7mm Mag in well-trained hands will do the job. The 7mm STW is a superb long-range chambering, but it will knock the "snot" out of you . . .

. . . same for the 7mm RUM.
A point to ponder . . . I have never shot a deer over a hundred yards . . . I probably wouldn't either . . . I can always get closer or wait till another day for that good shot.
There are as many opinions as there are people on this subject