Handguns, other than muzzleloading, must have a barrel at least 4 inches long and must fire a bullet of .243-inch diameter or larger. The handgun cartridge case, without the bullet, must be at least 1.16 inches long.
Full metal-jacketed bullets are not permitted.
Handguns are not permitted on any military areas.
From what I understand you should have no problem using a pistol like this one.
Leupold Ultimate Slam scope. With practice you can shoot 300 yards. You'll have to figure out the wind hold for your set up though. The other slightly more expensive option would be a Leupold with a custom turret made for your sluggun.