Opinions are like,uh, navels, everybody's got one. Here's mine,based on lots of experience and training.
Shotguns are potentially the best approach for HD. I say potentially because after 10 years as an instructor, I've seen no one move past bare minimum proficiency unless they LIKE to shoot shotguns. If you hunt, shoot clays, skeet or trap, a shortbbled, fast handling shotgun may be the most effective weapon for inside 25 yards. If you don't,look elsewhere.
And, a HD weapon has to be effective in all hands that may need it in your family, Neither Wife nor Daughter like shotguns, so there's alternatives here for them. The 870 is mine...
And, safety has to be mandatory, If there's kids or irresponsible adults that may have access to a stored weapon,you need to figure out a way to keep the weapon accessible, but away from the wrong hands. Gun safes, trigger locks,etc...
You mentioned cost. There's millions of used DA handguns out there in 38 and 357 at reasonable prices and with generations of service left to them.S&W, Colt, Ruger,even Dan Wesson, all have examples on the market with great value and worth.While the crunchentickers with the mega mags get the press, revolvers just keep on working and working.
And, to another person in the house that may need to use a HD weapon, revolvers are easier to train to proficiency than the autos.
Hope this helps...