Least expensive, scope-able repeater, bolt action? Maybe a older Cooey 600 (tube-mag fed)
Least expensive but accurate auto-loader? Marlin 795
Depends on the "budget" itself. Old Cooey single shots can be had under $100 without looking too hard, but adding a scope isn't really an option. I think for a modern-ish production gun, maybe the Marlin XTs or Savage Mark IIs. If there is a little more $ to throw around, one of the new Savage B series would be my suggestion, though I've never fired one. (I have had several Savage rimfires though, mostly decent accuracy)