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.
When you go home, tell them of us and say:
"For your tomorrow, we gave our today."