Northern Shooter, Brickburn gave some good advice for Alberta. I've hunted for all the species on your "either - or" list except brown bear. I really think the location, and local situation makes a big difference. I was a moose hunting fanatic for many years. Hard-hunted moose in wilderness are a very worthy quarry. Hard to find, hard to approach, and hard to deal with after the shot. Paddling and portaging a canoe into deep wilderness with a light camp outfit and a good companion is rewarding in itself. I've only killed a half dozen moose in about 20 "self guided" hunts. I hunt the easy ones in the farm land lately, they taste just as good.
Elk are exotic and difficult for most people. I've killed just over 30 now. I like eating elk, so I hunt where I know I'll be successful.
Mountain goats are the only animal I've hunted with dedication and planning and perseverance, and failed. Every time. In fact mountain goat hunting almost killed me twice. If you're young, tough, and determined, I'd say goats are the biggest challenge in Canada. Mountain goat country is quite unreasonable. Remote, very steep mountains covered in thick bushes, giving way to loose scree slopes, and eventually rocky crags and cliffs where the big old billies hang out. That's an easy place to die from falls, falling rock, land slides, snow slides, hypothermia, falls, bad weather, and perhaps heart failure. If I was 20 years younger I'd still be trying.