If you live in a rural area you probably aren't following me. I'm expressing urban/suburban reality.
I was obliquely pointing out that shotguns are huge, and bringing them down to reasonable size involves paying the tax man $200. Unless you do that, you have a very difficult time using a shotgun for anything but home defense and licensed hunting of in-season game, and even that may be difficult depending on your living situation.
Uncut shotguns must be disassembled and packed into non-gun cases (baseball bags or whatever) to safely move from the house unless you have an attached garage. Even there you must be careful - people will break into your house to steal musical instruments and sporting equipment almost as eagerly as they'll break in to steal guns.
In my world, a shotgun is a special-use luxury. A handgun is far more generally useful. That's because I'm basically urban.
I live in an urban area and cannot agree LESS.
Okay, obviously you don't want to be attempting to do house-clearing with a 30 inch goose gun. Still, this attitude that any shotgun with a barrel longer than 14 inches is unsuited to home defense is absolutely silly.
Take a look at the shotguns we used in the trenches and were used by police departments for the past 80 years. Most of them were sporting 20 inch barrels, and people were clearing houses with them just fine. It has only been recently that people who routinely kick in doors in hostile houses have decided "if 18-20 inch long is good, then 12-14 inch is even better!"
While I fully agree that '14 inch is better!' the degree to which it is better in active house clearing is extremely small. And also, active house clearing is the ONLY roll where 12-14" inch is better. (Concealability isn't a roll...it's a trait)
Finally, when I think about 'home defense' I don't think about actively clearing my dwelling of potential hostiles, I think of getting people to the bedroom, one calls 911 while the other points gun at bedroom door from the furthest corner from it. In such a set-up barrel length doesn't come into play. The one place it MIGHT is leaving the master bedroom to collect children, and even then I'd rather have a 20" shotgun than a handgun.
a 20 inch shotgun can be used with slugs to hunt deer, it can with harder lead slugs be used for bear defense. It can be used with fun at the range blasting pumpkins. It works great for home defense. It works great for clearing a house (although yes, a 14 inch version would be slightly better), it can dispatch that skunk or raccoon that is likely rabid, and it can be used for hunting squirrel, rabbit, and the like. It can even be used to take bird on the wing even though it doesn't point and flow quite so naturally as a nice 28 inch barrel would.
As far as being able to 'secret' a handgun better than an 18 inch shotgun...that's really a flaw of your community not the shotgun. Besides even if you have to 'secret' a gun around I disagree that the challenge of doing so with the much bigger shotgun is enough to offset the fact that a shotgun is so much more potent and versatile than a handgun.
For starters, if you absolutely had to break one down to transport it to and from the car, why is that so killer? Single and double barrel guns are EXREMELY easy to break down. My suggested bolt action shotgun cut down to 18.5", often a just a pair of screws (one behind the trigger guard and one in front of the mag well) hold the gun proper to the stock. If moving the gun from car to home needs to be done 'in secret' with great frequency I'd go to the hardware store and get a pair of thumbscrews of matching thread and length for less than a dollar and be able to take the stock on and off with no tools. Now you DO have something that could be thrown in a raquetball bag.
But honestly, left at full length you could wrap a rug around the case, or put it in a long box then for all the neighbors would know you bought some new curtain rods, blinds, or maybe a lamp. If the place is so gun unfriendly you could use one of those rectangular hard side gun cases and most would assume it was a guitar or something like that not a shotgun.
Still...keeping with the 'cheap' theme a nodescript box like blinds come in would be more than enough to keep your 'secret'.
Regarding carrying the gun around to 'stop a rape'. More and more states are getting the picture going 'shall issue' on CCW. However many of those places require classes and a license both which add up. If we are really doing a 'budget gun' then unless you are choosing a $200 handgun because that leaves $100 for CCW classes and license, then the number of handguns available at that price point drops dramatically. If you take the stance of 'well you can conceal without the permit' then that is true...but then you can also saw off your shotgun without the paperwork too. I am answering assuming the person is going to be law-abiding with their gun. While I totally agree that a 38 special to the skull will effectively kill a deer, I don't think I know of any place where it would be a legal hunting gun for deer. A shotgun with slug is legal all over the place for deer hunting. Shooting rabbit and squirrel with a 38 revolver is indeed legal most places, but a shotgun and #4 birdshot is a heck of a lot more effective.
Finally..
You are NOT going to find a perfect gun for all rolls at $300. You aren't going to find a perfect gun for all rolls at even $3000 even with a free pass on all NFA rules.
But regardless of the price, the shotgun comes closer than any other to covering all the bases.