Gmarr, am I correct to presume that your 300 H&H is a pre-64 Winchester? If so, and if it were my rifle, I would want to put a scope on it of similar vintage; probably the best Weaver K-4 or K-6 steel-tube scope I could find within reason; and similar appropriate rings and mounts. If the rifle has sights, I would consider quick-detach mounts. Other than that, I really like Leupold 3-9x40 scopes and would not have anything bigger. I would probably also look into a correct-vintage Redfield or Lyman receiver sight because, dang it, they just work so well. How about a picture or two?