No reason is needed for a shotgun certificate, although your FEO (firearms enquiry officer) will no doubt ask you anyway. A simple answer of 'clay pigeon shooting' will suffice.
You'll need a lockable cabinet/safe to store it in which must be bolted to a solid wall and out of plain sight.
You'll need to disclose any previous offences (no matter how minor, 3 pts for speeding etc) and give permission for your gp to be approached, medical records etc.
You'll then need someone of good standing (doctor, lawyer etc) to be your referee to vouch for you and also sign the back of your passport photos to say they are a true likeness of you.
Once all that is done your FEO will come out and visit you at home, informal interview, make sure you know the rules about shotgun ownership (carrying it in public, transporting etc) they will also check your security arrangements and make sure your safe is secure.
Few weeks later you should hopefully have your shotgun cert and you can go shopping!
You can have single barrel, double (side by side, over & under) pump action, semi auto etc but the magazine must not hold more than 2 carts (and one in the breech - 2+1)
It must be minimum 40" length and barrel no shorter than 24".
Pistol grips, rails, laser dot sight etc are all fine.
Whatever you do...do NOT mention home defence, zombie invasion etc as reasons to want one. You'll be refused and probably referred for psychiatric treatment.