I am not snake eater but I have lived and worked in war zones and the best defense firearm for killing people is one that will do the job more often than not.
Assuming you do not live on a ranch..like I do..albeit a small one.
I would suggest a revolver because they are fool (us) proof and are cheap like you asked.
Rossi makes some fine ones in .357 including I think a 7 shot version...nice which also shoots .38 for practice
.357 is a very lethal pistol cartridge
folks here suggest scatterguns all the time but my own experience is they are unwieldy in a home and the pistol grip version are foolish but for the most trained hands
if you do indeed live rural and need to defend open property then a nice lever action in any .30 caliber will do with reasonable glass...plenty of smaller cartridge black guns out there but they are likely more expensive then a Marlin or Savage lever or if you must an SKS or Romanian AK
and birdshot to kill people in shotguns...hilarious again
go outside and shot some number 8 or 9 at 20 yards and then try any type buckshot and see for yourself penetration and spread...I mean really
freeper advice on guns sometimes proves some people here are full of crap but a shotgun with buck in very trained hands with a coach barrel is not without merit...but still unwieldy
there is a reason CQB military assault teams use MP-5 and Ingram style mini carbines (small..fast shooters) ...for spray and swing ease..but they are not cheap
You aint breaking in and spraying a room full of people.
One or two are breaking in and you are spraying them.
I stand by the 12 ga.
As to any rifle, any shot outside of 25 feet is going to be questioned.
I don’t use rifles for home defense.
I have some nifty carbines, .30,9mm and 7.62x25 but it is just to much for home defense.
BTW, that nut job in Colorado did all his damage with a shotgun loaded with 00 buck.
His AR jammed
I like a short, hammerless revolver just because you can shoot through your pocket with it at close range, more than once. I had just about given up on packing a wheel gun when that though struck me, and now we have a couple of them. At 3 ft., .38 Spl +P will get the job done.