Based on your options, 325 WSM provides the best performance for moose. 300 win mag is a longer range version of a 30-06. Which begs the question, if your not shooting over 200 yds, why pay the extra price in recoil and muzzle blast, just get an 06, which is a fine moose gun properly stoked. Benefits of a 300 win mag, which is a fine cartridge, are really evident at longer range.
300 ultra mag is a highly specialized, flat shooting, ultra long range caliber with lots of muzzle blast and recoil, even moreso than a 300 win. No real benefit to this caliber in my opinion at ranges under 400 yds.
325 short mag is in my opinion the most interesting of the WSMs, as it provides serious medium bore frontal area and sectional density combined with very flat trajectory, in a short action package. 350 rem mag does the same thing. recoil and muzzle blast are up there, but there is no free ride. All things being equal, I believe that medium bores do a better job of knocking down larger game than the 30 cals.
If I had the cash, I think the Browning BLR stainless laminate lever rifle in 325 short mag would be tough to beat as a moose rifle. That said, the 300 win mage in just about any configuration would also be a good choice.
In my view bullet choice and construction is much more critical than caliber. With premium bullets such as barnes TSX or Nosler partition, even low velocity calibers like 35 rem and 30-30 become decent moose killers at 100 yds or less. Likewise I have seen bargain priced factory ammo in a 300 win mag do a terrible job penetrating in moose broadside at 150 yds. Buy a rifle you are comfortable shooting and can shoot accurately, use quality ammo designed for what you are hunting, and you will do fine!