I am familiar with the Savage 111 "Light Weight". A buddy of mine bought one in 308 Win.Rem. It has the Accutrigger. This rifle ended up to be a very accurate shooter once we found the best factory load .... for this one it turned out to be a Federal Premium using a 165 gr. Sierra Game King bullet. Shot group after group in the range of .75 to 1.25 MOA. I consider that excellent for a factory grade rifle and non custom loaded ammo. Of the scopes that you mentioned, I think that you would be well pleased with a Leupold or Elite in your price range.

I am not familiar with the Weatherby rifles these days having shot only one older Mk 5 chambered for 300 Weatherby Mag.