All shotguns kick, Driven, some more than others.
Recoil tolerance varies SO much it's hard to point at one setup and intone "This is what you need" in stentorian tones.
I shot a 20 gauge 1100 once, the Special Field model with 21" bbl. I thought at the time it would make an outstanding HD arm.It still kicked more than my HD 870, which runs about 9 1/2 lbs ready.
The 20 Gauge 870 YE I got for the kids is vicious with heavy loads.I'd want to add a half lb in weight before recommending it as a high volume, "Serious" shotgun for the average gunnner.
To cut kick, use a heavier shotgun and a lighter, slower load.
The disadvantage of a 20 gauge for a HD/CD shotgun is there are less ammo options than the 12. #3 Buck is the sole buck load, and maybe half the 12's variety with slugs.
If you can handle the weight of a 12 gauge semi auto, the Remington 1100 and 11-87 and the Winchester X2 are available in short bbled, police style versions. Kick is a lot less with gas autos, which is the REAL reason for their popularity.
HTH....