Shot placement and comfort with your gun is more important than caliber size. If not used to large calibers, get a 30-06 and shoot, shoot, shoot. Pleanty big to knock down moose and all but the biggest bears.
If you can handle it, shoot something larger like a 300 win mag but again, shoot a lot. Don't buy a large caliber, shoot it twice and head up here. Lots of recoil with a 338 or 375. If not used to it, will be less likely to want to practice and less likely to make a proper shot placement when it might be offered.