Re: Do you know...
Let's tackle "why?" first. Even in the UK owning a shotgun is hardly unusual, though it's nowhere near the level of ownership in the USA (more on which later).
Shotguns are useful for vermin control, sport shooting, some hunting, and 'home defence'. Rifles are primarily useful for sport shooting and hunting. Handguns are useful for some hunting, target shooting, and as a side-arm ("To fight your way to where your rifle is").
There is a saying here: "When seconds count, the police are just minutes away." Bottom line, the USA is not the UK. It's much larger, and though its population is about six times larger too, even in the cities population density is lower than the UK. In rural areas, even ignoring Alaska, it's very low. Self-defence is not all about "shooting the bad man", there remains dangerous wildlife close enough to settlements to be a regular, sometimes weekly for some people, nuisance. Go off the beaten track a little, or live on a ranch or similar situation and it's arguably negligent *not* to have fast access to a firearm for defence from dangerous animals, in many places.
Now the cultural stuff - It's enshrined law from a principle it inherited from the UK, specifically English law. It's actually the UK which has shifted hard in the other direction, not the USA that has suddenly gone "gun mad", though there was always more of a "gun culture" here, given the historical realities. That law is an amendment precisely because the original 'framers' of the constitution felt it was so blindingly obvious a right it did not need to be spelt out, but some states attempted to restrict access and ownership, resulting in the second amendment. A similar story exists with regard to the first.
In Houston, you could buy a shotgun or handgun, after being checked by the FBI against their database (the 'background check' you hear about a lot) to confirm that you are not prohibited from possessing or purchasing a firearm at that time. There are many ways to be so prohibited, from the essentially permanent prohibition for violent felons, to temporary ones for people facing certain criminal charges, etc. No "pass" from the FBI, no sale (and likely a visit to your home address from said FBI).
No private citizen can own an M16 - that is a military designation for a weapon based on the Armalite AR-15 rifle. It's also not an "assault rifle" (it's debatable if that term even has meaning), it is a ''battle rifle".
A nuclear weapon would be excluded by various laws, including the prohibition on owning "destructive devices". Basically, it is not considered a personal weapon, the law in question is about ownership and possession of personal weapons - "arms".