For shots to about 100 yards my favorite rifle is a flintlock. Just a cool way to bring home the meat.
But for short range it's pretty hard to beat a 30-30 or 35 Remington. And revolver shells in carbines (357 mag and 44 mag) work great too.
Of course any gun is OK if you gave a safe backstop and a bullet that opens up fast and isn't very strong will make a close range deer rifle out of a 300 Mag with little danger to the neighbors too. Just hard of deer meat.