As far as a muzzleloader out to 300 yards goes, you are pretty much getting into smokeless capable muzzleloader ranges. Past 250 with Black powder or BP Subs such as BH209 you are getting awful weak on speed. Just not as much energy as one should have at 300 yards to CONSISTENTLY penetrate bone and muscle.

There are a few options that are smokeless rated (meaning you can use smokeless powders) but you are not going to find many, if any, that are in your price range. Most of them would be over $1000 just for the rifle alone.

Or, if you have something like a Savage 10, TC Encore, CVA Accura, Rem 700, you can have either a barrel made (TC, CVA) or have it converted to a smokeless MLer (Savage, Rem 700) with a barrel and different bolt. If you already have the platform (rifle) then you MAY be able to squeak into your price range. Can definitely come in to it with the TC or CVA since all you need for them is a barrel.

Now the rifled shotguns, out to 300 you are looking at a dedicated slugger NOT a shotgun with rifled barrel conversion thrown on it. Those are fairly accurate but not the best in the world. The Savage 220 or 212 (20 gauge and 12 gauge) is about the best dedicated slug gun on the market and falls well within your price range. Around 650-750 for the gun leaving around 250-350 for a decent quality scope.