99% of shotguns _could_ claim both purposes - you need to consider where on the spectrum of "sport" (what type?) and "home defense" you are willing to sit.
I would suggest a pump action for hands-down reliability but many sporting guns are semi or double barrel for faster follow up shots.
A tighter choke is good for "sporting" birdshot but my "defense" shotgun uses no choke at all.
In terms of barrel length, I have used my 20" "defense" gun for shooting clays and found this to be the least restrictive aspect of the "defense" gun - I was more bothered by the pump-action, less so by the lack of choke, and least of all by the barrel length.
Luckily, shotguns are the perfect do-anything gun. Get a 20"-24" pump action 12 gauge with a relatively open choke and a front bead sight and call it a day.