Savage over Remington just because I'm not a Remington fan, even though their action is right up near the top. NO, the .243 is not designed for that kind of yardage for clean, humane kills on deer size game, but it will do a number on antelope with 100 grain ammo at half that distance and to varmints with smaller grain ammo designed specifically for that purpose further out. It will not buck the wind like a 25-06 and bigger calibers will, so that also comes into play when you're talking distance shooting. If you're looking for long range calibers for deer and bigger, you need to go up the ladder a ways. Here is a quick synopsis taken from a ballistics website I like:

The .243 produces its fastest kills inside 200 yards or at impact velocities above 2650fps. Inside this range, internal wounding with select projectiles can be incredibly fierce with lung wounds as wide as 3”. Beyond 200 yards, animals may show little sign of being hit and are able to cover considerable distances regardless of wounding. Out at between 300 and 400 yards, the .243 is still capable of producing a wide wound channel through vitals, usually around 1” in diameter. Nevertheless, wind drift can make exact shot placement difficult, leading to very slow kills. Rear lung shot game (40-60kg) can take several minutes to expire.