I can't advise on which shotgun to get as I shoot BP rifle and pistol.
You do not necessarily have to buy a shotgun, a musket would do the same job, a calibre being approximately 20 bore would be better to use as a shotgun. And, if you go to a rifle range you will be able to use patched ball instead of shot. This also applies to larger calibres, 12b, 10b, etc.
You will need a an "Explosive License" to purchase blackpowder. You can apply to the FEO for this, it does not cost anything.
Once you have this you wiil need to send for an "RCA" document from the HSE so you can purchase/carry loose blackpowder.
You will also need a wooden box to store the blackpowder.
Try looking at blackpowder shotgun sites to find out what charge you would need.
In the old days it was common to fire 1-1/4oz of shot with 3-1/2drams of powder in the 12bore. (Approx 96 grains).
You may find lower charges suitable so exploring sites might give you the information you are looking for.
Over the powder charge you need a card and a wad, the shot, and then another card to stop the shot rolling out.
Hope this helps.