You can't go wrong with a 10/22, if you can find one in your price range. Another one I'm curious about, just price-wise, is the Mossberg Plinkster line. It looks like they have dozens of varieties, options, and prices, but the entry level models sell for $150 to $200. I have never read/heard anything about their quality and reliability, but it might be an option.
Good luck and take care.
Good luck and take care.