Sounds good to me. Probably about $300.
You could also go with a lever in .30-30, which you should be able to pick up under $300 easily. I suspect bolt action .30-30s may sometimes not feed as well as levers, but then you do have the option for spitzers.
Another option would be a new single shot, such as the H&R/NEF Handi-Rifle in .30-30, again around $300. A repeater is probably more humane than a single shot though because you can dispatch faster if a follow-up shot is needed.
A bolt action in something like .257, 6.5 (Swedish) Mauser, or 7x57 Mauser would probably work well. You should also be able to pick one of those up for under $300 if you shop around.
If you're open to semis, you could probably move up to the .270 or .308 range because the felt recoil will be less with a semi but then you're talking more money, probably over $500.