The .223 is basically ideal for this situation. Built properly it will keep up with everything larger out to 300 yards and if you don't need accuracy you can find factory ammo cheaper than any other centerfire rifle cartridge.
I prefer the Remington 700 for its ubiquity but the tikka t3 sporter with a 1:8 twist barrel (which is well above your price limit) is practically perfect for a .223 all purpose rifle.
You will know better what you want but I think a .223 with good stock which allows for slung positions and adjustability, a magazine feed, and a fast twist (1:9 or faster) will provide you with every opportunity to shoot targets in any format out to 600 yards. Such is the ideal center fire trainer.
I prefer the Remington 700 for its ubiquity but the tikka t3 sporter with a 1:8 twist barrel (which is well above your price limit) is practically perfect for a .223 all purpose rifle.
You will know better what you want but I think a .223 with good stock which allows for slung positions and adjustability, a magazine feed, and a fast twist (1:9 or faster) will provide you with every opportunity to shoot targets in any format out to 600 yards. Such is the ideal center fire trainer.

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