For 600 yard target shooting and 300 yard deer hunting the .308 or .30-06 is hard to beat.
The .243, or even better 6MM Remington is an excellent deer rifle to 300, but would, IMHO, be a little light for 600 target, especially if you live in an area with any wind.
In between calibers like .25-06, .270 etc will do the job, but do not give you the bullet weight selection of the .30-06.
Unless you are a VERY experienced rifleman, I would avoid magnums like the plague.
And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth.