17hmr is useless past 200yds and wont even do that in a light breeze. 7.62x39 will make 300yds with enough practice but i cant think of anyone that makes a target rifle in that caliber.Cz makes a nice little carbine in that caliber but its not really a target gun and most ammo in that caliber isnt known for shooting tight groups.7.62x54r is another old soviet round and while it will shoot well past 300yds with ease and ammo is inexpensive you will mostly only find it chamberd in mosin nagants and they can be really hit or miss as far as accuracy is concerned. If you could find a PSL it might do what u want but they still are not tack drivers. Your best bet is a bolt gun with a heavy barrell. The heavy barrell will help keep the barrell cool at the range and will also help add stiffness to the barrell both aid in accuracy. Look at a savage 10fp, rem 700sps varmint or tactical,or marlin x7vh. as far as caliber 308 is a common target round and also good for big game hunting. 223 is cheaper and u can hunt varmints with it and some states allow it for deer but good luck finding any right now. In todays climate 22-250 might be the cheapest that would meet your needs but again it is marginal on game the size of deer.
Kill em all and let God sort em out! USAF