I don't know how target shooting differs from the shotgun sports, perhaps you're now shooting rifles and handguns at paper. The selection of which shotgun sport to concentrate on is much a matter of which best suits your personality, your natural abilities, and what's available locally.
Give them all a try and shoot the ones your like -- there's no rule that says you can't shoot more than one of the clay sports. Most of the shooters, I know, who've taken up shotguns after rifle and handguns wish they'd tried clays earlier. I suspect you'll feel the same.