For the game you mentioned the 25.06 would also be a good match. It is an excellent cartridge for long range small game up to deer/black bear sized animals.
If you expect to use it for larger game lean towards the 6.5- 7mm/.270/30 cal cartridges.
If you will only use it for smaller game the .22 centerfires/6mm/.243 will suit you.

Good Luck