Don't get sucked into the whole "You gotta go .338 man, it's like a mini 50 cal. Way better for 1000 yard shots on elk" Only fools and TV shows shoot that far.
Ask yourself why the .308 is STILL used by the US Military, still one of the most popular hunting calibre's, why you can buy it ANYWHERE. Because it works. There are SOOOO many loads for any sized animal in North America. You want a heavy bullet ?… you CAN buy 220gr - 240 gr, but that is HUGE for a .308, better loading a 185-190 well. Not much going to stay up after a .308 - people drop elk and moose with Bows - so why would you think a .308 is too small ??? --- hahahaha
THe 7mm Rem Mag is the next best choice. FLAT trajectory, Hauls butt (fast round), carries a LOT of energy. Kicks a bunch more than the .308 - but a great round.
(.223, .308, .7mm Rem Mag)