quail hunting games

Home defense to hunting shotgun?

I bought a Mossberg Persuader for home defense. It has a 20 in. barrel and a fixed choke. That was the main purpose for the gun, but I was thinking of starting to hunt aswell. Im mostly interested in small game like, rabbit, quail, squirrel, etc. What is a good barrel size for small game and choke type. Also, is there anything this gun setup can be good for right off the bat? Thanks.
If I just bought a 28″ barrel with adjustable choke, wouldnt that be the same as if I bought a mossy 500 set up like that anyway?

I have the same exact shotgun you have —- Its a great firearm but that particular model with a 20 inch barrel doesnt allow other barrels to be put on it….. The magazine tube is too long….. The other Persuader Cruiser models that have the shorter magazine tubes can accept different barrels but not the 8 shot models….. Its not cost effective to change the magazine tube for a shorter one…… By the time you bought a shorter tube and barrel you pretty much have spent near what a new shotgun would cost…… Do what I did! Buy another Mossberg 500…. Mossberg makes a field model that has 2 barrels included…..

Bobwhite quail hunting Kansas