I'd look at e-bay,at least.
A used Leupold still is under Leupolds service policy.
There are a lot of Weavers,and a fair number of Denver Redfields.
Opinions wll vary,but mine is this.If you are shooting a 30-30 you are unlikely to be shooting much over 150 yds,maybe 200,stretching it.
IMO,a fixed 2.5 x,or 3x,would be plenty.4x tops.I would not look for a variable on a budget.
If you can find a one piece Weaver base,you will likely get good ring alignment,and it will be trouble free.Weaver rings are cheap,light,and strong.
On e-bay,there are a few dealers with new old stock in the Weaver mounts/rings.I'm not sure how lo-scope friendly a 340 bolt handle is,look into that before you spend money.Mount your scope as low as the bolt handle will let you.
You might try pricing the new Weavers,Redfieds,etc in a 3x You might find a pretty reasonable price.
You will want to be able to close your eyes,shoulder the rifle,open your eyes,and be looking through the scope,clear and centered.For this season,that might mean putting alittle foam pipe insulation over the stock comb and wrapping tape over it.(ugly?yeah.You do not have a lot of time for pretty right now.It comes off.)Or making something of leather.
And,do not get the scope too near your eye.The scope will cut you during recoil if you are too close.
Good luck!