This year I switched from a 300 WSM to a 270. I've used the 300 the last few seasons with handloaded 168 grain BST bullets and have lost way too much meat to the high-velocity bullet, even though the load was a minimum load. I must admit, I was romanced by all the press. The 300 WSM is really a 300-yard cartridge.
I'd say the answer depends on the range at which you hunt. For 250 yards and under, I'd use a .270. For 250 yards and over, I'd go with something larger.
I think the top 3 selling cartridges in the world are .270, 30-06, and 7mm Rem Mag, so you really can't go wrong with any of the three. I'd say .270 for short range, 30-06 for mid-range, and 7mm mag for long-range.
If it were me, I'd start with a .270 - the original flat-shooting cartridge.