Re: Need advice on budget scope for 338 RUM
Well you clearly are not just gonna get rid of a rifle you just built, and if money is a factor and you are thinking $500 ish, i would look hard at the various vortex offerings, Some Nikons in the 400-500 range, and Sightron offers some fix power scopes in the 500 range but tend to have smaller objective, but they should be guaranteed to hold up on the 338.
Don't worry about crazy high magnification in that price range as your sight picture will be fairly poor at the high magnification with the scopes in that price range anyway.
JMO, but a decent scope, use it on the 338 for a while and if you get some funds later down the road, more that scope to something else and get nicer optic for 338.
good luck