Most of the “specialty rounds” are junk.
Stick to conventional buck and slugbarrel
As to what shotgun to get, go hit your local gun shop or pawn shop.
Go take a good look at a used Mossy/Reminton/Winchester/Ithaca and have the barrel cut back and the bead reinstalled.
You’ll likely have well under $300 into it, if it gets put into the evidence locker you’re not hurting and if it gets dropped, beat up or covered in muck you don’t care as much.
Don’t try to make a rifle out of it, simple is best.