The .243 works fine on deer. My son and I each got one two years ago, and we've taken seven deer with seven shots.

As far as being "discouraged" about a .30-06, and then getting talked into a .308... How did that happen? The .30-06 will do everything a .308 will do, and will do it with just a little more power, a little faster, and a little flatter trajectory. And, the .30-06 can handle 220 gr. bullets as well. This would be an advantage in favor of the .30-06 if you wanted to use it for the big bears. It's hard to find .308 factory loads using bullets larger than 180 gr. The .30-06 is plenty of gun for moose and elk. The .308 is a fine cartridge, and will do everything that you have asked about in this thread. But, the .30-06 will do it all just a little better. The only advantage in getting a .308 is that you can get it in a short action, so your rifle will be about an inch or so shorter. This can be a small advantage if you hunt from a blind. Whichever of the two you choose, the game won't know the difference.

If this is your first rifle, I would avoid anything that says "magnum". Recoil and noise are not your friend when you are just learning to shoot. Ihunt from a blind, so I've developed aslight preference for the short action cartridges. The .243 and .260 are both good rounds if you're interested in coyotes and deer. For the bigger stuff you've listed, they'll work, but, it's reallly better to add a little more power, so take a step up to the 7mm-08 or .308.