Depending on what your gonna do with it , as far as shooting what at what range would dictate a bit more as to what caliber I'd pick.
when you say 270-338 I assume that your meaning to neck down the 338 Winchester case to 270 and not mean necking down the 338 Lapua case to 270.?
The 338 winchester is a great case to build on but their is limited amount of good brass , theirs nothing that the 270-338 could do that a 270 Wby coulden't do with factory loaded ammo. So you would be having to shoot only handloads with the added expense of custom dies and the extra effort of necking down the cases.
if you just getting into shooting longe range with a bigger rifle then I'd say have that gun rechambered to 7mm Rem mag , you will have plenty of readly available factory ammo , dies that are easy to find and cheap compaired to the 270-338's without the added hassel of the case forming.
Another great option is the 300 Win mag with the same features as above.
Or you could have a bit more work done to the action and get a bigger RUM based round.
