For me:
Some kind of decent .22- this is for plinking and small game, so I would likely stick to a 10/22, probably built with better bits. Alternatively, .17 hmr gun
Medium/large game. I'd stick with the standards- .270/30-06, something similar. If you also want to use it for target/range, maybe compromise to a .25 caliber or similar power
Bush gun: 45/70, 444, 450, etc. light, quick, big bore.