Hi Jerry
In no particluar order, here are some comments about the various milsurp calibres you listed.
1. 6.5 Carcano - Nothing wrong with it, just the slowest of all the bullets (160 grain at about 1900 - 2000 fps) and probably the hardest to shoot accurately. The Carcano is capable of quite good accuracy, however, the sights on any Carcano that I own are not so good. Unless you shoot this rifle well, I would leave it at home.
2. 6.5 Swede - Once again, there is absolutely nothing wrong with this calibre and the Swede Mauser is generally a tack driver. The 160 grain bullet in this round has good stopping power. Lotsof Moose in Scandanavia have been downed with this round.
3. 7.62 Russian - Sellier and Bellot makes a nice 180 grain package for this gun and it would do quite nicely for moose. It is hard to find, and if all you can find is the 150 grain Bell/Igman, then forget it. 150 grain is not a good moose choice.
4. 7.62 x 51 - Good choice, with a larger bullet zand you should be able to find ammo just about anywhere (165 grain or 180- would be my choice). My only comment is what tyype of rifle do you have? If it is a weak actioned 1916 Spanish Short rifle then I wouldn't want toshooot fullhouse 308 load in it. I also would not want to fire 180 grainers through a M14 clone either.
5. 303 - 180 grain bullets and you would have a good moose gun.
As mentioned, all of these rifles are capable of dropping a moose, Personally, I would take the one out of the list that I could shoot the most accurately, with the right round. Nothing under 160 grains in the 6.5's and I would stick to 180 grains in the 30 calibres.