If you want to go this route, go shorter and acquire a AR15 platform pistol, that will relieve you of the need to get the needed NFA paperwork for a SBR.
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There are a number of manufactures that produce this format, in a number of calibers 5.56X45, 7.62X39, .308 Win just to name a few.
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Most of these will also cost you less than just about any SBR available, usually right at a grand. My SGM9 is right there if I need it, but I also don't need to worry about neighbors, I live in the country away from the so called civilization. lol
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There you have your trip into fantasy firearms that just aren't necessary to protect your home when a $200 shotgun with a minimal barrel, open choke, loaded with buckshot will handle the reticent criminal that wishes to be stupid on your property.
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PS. 20 gauge and .410 gauge shotguns will provide the same protection and will be easier to control when fired. Once you buy make sure to practice and be comfortable with discharging the weapon so there is less surprise when it goes off your adrenaline will be running high enough as it is.
True! I recommended the AR platform because of the reduced lethality to bystanders in other rooms of the house over a 12-gauge and the other mentioned firearms, and because you have 30+ rounds at your disposal. If you live alone, in a house, in the country, 12 gauge buckshot is just fine, but a $200 shotgun will probably be a double barrel. That's two rounds, which for me personally is not enough for home defense. A nice 870 with 8 rounds and birdshot is probably safe and effective. Just remember, you still have to point the weapon at the bad guy. The shotgun will not spread out 10+ inches at home defense range. You have to "aim" it like any other weapon. AR or shotgun, at 10 feet, point and shoot works equally well.