For afforadability and accuracy...I'd go with a .223,.204 or even a .22 Hornet?The .223 will reach out pretty far and have plenty of knock-down power even if it gets a little windy...the .204 is a very fast and accurate Rifle and it reaches out even further when need be,the .22 Hornet is another small center-fire Rifle that is easy on the pelts/hides.Each of these Rifle are fairly affordable....the .223 would be great in a Savage Light weight Hunter Model 11 or 111 bolt-action and the .204 in a CZ-USA model 527 "American" would make a great Walking Varmint Rifle....even a .223 in a CZ-USA would be an awesome Rifle and each of these I mentioned can be bought for around $600.00,then You have to add mounts and scopes of your choice.
The .22 Hornet are made by CZ-USA,Kimber and I believe possibly Savage too?A .22 Magnum would be a good choice but its not going to reach out into 200-400 range that well.Next up would be something in a .220 Swift or a 22-250 thats going to reach out further and have more knock-down power......a .243 is a good Caliber also,just need to get a lighter grain bullet in say a 50-60 or 75 grain?