Not really enough terminal difference between the cartridges you mention to be worried about.
All of them are perfectly capable of doing what you desire IMHO.
Still, if you just have to justify something, my nod would go to the 243.
I have a 257 Roberts, Remington 700 Mountain Rifle and it's a great all around rifle. I've taken everything from Marmots to Elk with it.
I have a lovely, European commercial Mauser 98, 243, with double set triggers and a Pear Wood stock. I wouldn't hesitate to use it on anything from Marmots to Bears or Elk either.
I just finished building 22-250 on a Rem Mod 7 stainless action and the biggest mistake I made was not getting a tighter twist rate barrel. I used a proven accurate take off barrel and it shoots extremely well, if I do my part.
I may just bite the bullet and order a decent 1-8 twist rate barrel for it. The 1-9 twist barrel is OK and will accept bullets heavy enough to be legal for hunting big game in BC but I would like to shoot at least the heavy 90 grain offerings if it's going to be a multi purpose rifle.
