I am fortunate enough to have multiple chuck guns and shoot a good number of chucks each year (150-700). I have multiple guns for different locations, fixed shooting or walking and various yardages. One thing is for sure if you want to see your hits/misses you will need a heavy gun and a caliber 6mm or less unless you install a brake and the folks who's property you are on or near don't mind the extra noise. Here are a few of my picks and restrictions.
TC/Bullberry 22 Magnum with 33 Vmaxes for population areas good to 125 yards.
TC/Bullberry 17 Ackley Bee with 20 vmaxes out to 225.
22 Hornet Ruger 77/22 out to 250 yards with 40 grain ballistic tips and LILGun.
TC Venture 204 Ruger out to 350 with 39 grain blitzkings.
Rock River Coyote rifle shooting 53 vmax out to 300 (good for multiple targets).
20BR Savage SSS shooting 39 grain blitzkings out to 425.
220 Swift Savage shooting 53 Vmax out to 500
6mm/284 Custom Remington shooting 105 Amax out to 700
6.506 Custom Savage shooting the 140 Amax out to 1000.
For one gun 300-600 with most shots being under 500 I would go with the Swift or another large cased .224 without a brake (I hate brakes). Gun would be a repeater bolt action with a varmint weight barrel and heavy stock. Scope would be a variable with 4-6 power on the low and 16-24 on the high end.
Here is my 6mm/284 (Trued 700SA, sako extractor, flutted bolt, factory trigger adjusted, McMillian A3 stock, Flutted Krieger 26" 8 twist, Weaver 20MOA, Vortex Viper HST in Vortex Precision Rings). I shoot 55's at 4200fps, 87 Vmax and the 105 Amax all depending upon range to target. She would fit the bill!
Mike.