I favor the old Weaver scopes, had a k3 on a Marlin .45-70, use 2.5x Post reticle scopes on Rem 600 carbine .308 Win for woods hunting.
I never bothered to scope the 336 .30-30, but if I did, it would be an old Weaver (or JC Higgins
) 2.5x Post in weaver mounts & rings. Might not look the best, but are solid, rugged, and dependable.
As to scopes, you might try haunting the gun shows and pawn shops for used ones, to meet your price point. Decent new ones have pretty much moved above that.
Also, a word about variables. I do like them and use them, but if you put one on a woods rifle, where a snap shot is a likely possibility, you
will, at some point find the scope on its highest setting when you want & need it on low power. If you make a strong habit of checking the scope setting Every time you pick up the gun, it will help, but Murphy lives and never takes a day off, so a variable with a high power end (7x+) is a poor choice for a woods rifle, unless you constantly check it.