.300 wsm as a starting point...

up to .340wby?

.270 is pretty close to a 7mm rem mag IMO.

so if you do want to step up and have long range I'd start at the .300wsm.

stepping up to a .338 cal will definitely be a step up in bigger bullets etc...

I chose a .340wby for a similar situation, fast, big, flat.

but any 300, 338 mag would do a good job I think.