DR: aside from picking a gun that is appropriate, be it O/U, semi-auto, pump, SXS, or single shot (like the BT-99 that was mentioned), there is the matter of "fit". Shotguns, ideally, are fitted to their owners - certainly not everyone does this and many who do not shoot quite well - but ideally a fitted shotgun is the way to go.
This is because the shotgun, unlike other firearms, does not have a rear sight mounted on the gun. The rear sight is the shooter's eye. If the eye is to the left or right of alignment with the front bead when the gun is mounted, or is high or low relative to the bead.....the shot pattern will go left, right, high, low. When the shotgun is properly fitted and properly mounted, it will shoot where you are looking....you don't have to aim in the traditional sense.
I am a tall fellow also, with long arms....a normal over the counter 870, let's say, will have a stock that is designed for a person of average size...with shorter arms. The distance from the trigger to the butt on such a gun may be 13-14 inches. With my long arms, I need to have a stock that is over 15 inches, otherwise my eye is not going to be in the right place when I mount the gun......and that is just one of a number of measurements that determine fit.
Pete