To partially answer the first bit of your question: yes, people have always owned guns in the US; as a function of being a large country with a prolonged 'frontier'/colonisation period and a large rural and agricultural population. I couldn't find any particularly canonical long-term data on gun ownership, but the General Social Survey has monitored gun ownership levels since 1973, so you can get a sense of recent trends in gun ownership from that.

Now, on to the complicated part. This is an incredibly politicised issue, with wildly diverging viewpoints and interpretations of events, actors, the Constitution, etc. So it's very likely that there will be people here who view the below as liberal nonsense or historical revisionism. But here goes...

As far as I know, no state has ever attempted a complete firearms ban (most countries, even those with the strictest gun control laws, usually also have exceptions — for farmers, hunters, etc.)

Probably the most substantive and relevant recent attempt was the District of Columbia's Firearms Control Regulations Act of 1976, which banned handgun ownership in DC and introduced strict controls on the ownership of other kinds of firearms.

The reason this is so significant is that in 2008 the Supreme Court struck down that law as a violation of the Second Amendment in District of Columbia v. Heller, which is regarded as one of the most important gun control rulings in US history. They held, among other things, that:

1. The Second Amendment protects an individual right to possess a firearm unconnected with service in a militia, and to use that arm for traditionally lawful purposes, such as self-defense within the home.

But Second Amendment politics are actually even more complicated than the tortured state of the current US gun control debate would suggest. What's particularly interesting (and surprising for its absence from popular memory or understanding) is that the interpretation of the Second Amendment as comprising an individual, personal right to own firearms is much, much more recent than people generally assume.

Jill Lepore (professor of American history at Harvard) wrote a long and extremely interesting piece about the development of the Second Amendment in the New Yorker during the Trayvon Martin murder trial, in which she argued that the interpretation of the "right to keep and bear arms" as an individual right dates only from the 1970s. Previously, she argues, there had been a consensus interpretation of the Second Amendment as a collective right — ie. the right to form militias as a safeguard against government overreach/tyranny.

She describes a conservative takeover of the National Rifle Association (which had previously been "chiefly a sporting and hunting association" which supported some significant federal gun control laws — and at times actively lobbied for regulation at the state level) in the 1970s:

In the nineteen-seventies, the N.R.A. began advancing the argument that the Second Amendment guarantees an individual’s right to carry a gun, rather than the people’s right to form armed militias to provide for the common defense. Fights over rights are effective at getting out the vote. Describing gun-safety legislation as an attack on a constitutional right gave conservatives a power at the polls that, at the time, the movement lacked. Opposing gun control was also consistent with a larger anti-regulation, libertarian, and anti-government conservative agenda.

[...] In 1977, the N.R.A.’s annual meeting, usually held in Washington, was moved to Cincinnati, in protest of the city’s recent gun-control laws. Conservatives within the organization, led by [Harlon Bronson] Carter, staged what has come to be called the Cincinnati Revolt. The bylaws were rewritten and the old guard was pushed out. Instead of moving to Colorado, the N.R.A. stayed in D.C., where a new motto was displayed: “The Right of the People to Keep and Bear Arms Shall Not Be Infringed.”

Thereafter, the NRA became an increasingly powerful lobbying force and succeeded in making this interpretation of the Second Amendment a conservative shibboleth and Republican party cornerstone. This is legal commentator Jeffrey Toobin's summary of that process:

The re-interpretation of the Second Amendment was an elaborate and brilliantly executed political operation, inside and outside of government. Ronald Reagan’s election in 1980 brought a gun-rights enthusiast to the White House. At the same time, Orrin Hatch, the Utah Republican, became chairman of an important subcommittee of the Senate Judiciary Committee, and he commissioned a report that claimed to find “clear—and long lost—proof that the second amendment to our Constitution was intended as an individual right of the American citizen to keep and carry arms in a peaceful manner, for protection of himself, his family, and his freedoms.” The N.R.A. began commissioning academic studies aimed at proving the same conclusion. An outré constitutional theory, rejected even by the establishment of the Republican Party, evolved, through brute political force, into the conservative conventional wisdom.

To circle back to where I started: this debate reached its conclusion in Heller, when it became the law of the land, when SCOTUS confirmed the individual-rights interpretation as the law of the land.

It's fascinating, really — and the fact that the individualist interpretation of the Second Amendment has become not just consensus but outright orthodoxy, to the point where a historian reminding us how recent that understanding is becomes a revelatory act, is remarkable.