If you are truly on a budget I would suggest looking at H&R/NEF. You can get a single shot rifle/shotgun fairly cheap. If you are looking for a slug gun, get the 12 gauge ultra slug gun, and have them fit a 10 ga turkey barrel to it when you order it. You would be covered for both. If you want a centerfire you could get a centerfire version in the caliber of your choice ( I would get a .243 or .270) and then have it fitted with a 12 gauge turkey barrel. The H&Rs are decent rifle/shotguns for the money and if you get the right frame you can swap them from rifle to shotgun in a matter of minutes. The down side is they are single shots. You can also get a 20 gauge heavy slug barrel for it as well.

Paul