.243 win, 22-250. 17HMR if you want cheaper ammo. Also don't rule out a cheap rifle like a Mosin Nagant. They cost $100-300 depending on condition, the 7.62x54r ammo is cheap. For 200 yards 4X magnification is probably fine, but you could also get something like a 3-9X variable power for more versatility.
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