The first part is what you need; the second part is how to get there (it won't be pretty).
High Paying Jobs; Free Education, Healthcare & Housing; Benevolent Dictatorship; Regulated Borders; Redistribution of Wealth; Replace Immigration with Guest Workers; and Censorship
If you can provide these, then I can give you UAE as an example, remove their flaws and add extra protections to see if it fits your requirements for your story, although I will stress I do not find this a good way to live.
When we were living there, the Emiratis (citizens, representing 10% of the population) and the wealthy expatriates enjoyed a life of virtually no crime, sort-of gender non-discrimination, mostly gun-free, and public trust in the police & leadership.
Crime: Skilled expatriates like us were making 12k and more a month. Threat of breaking a serious law meant loss of job, loss of visa, deportation or desert-jail (that's what we called it). No way was I going to steal a car, because I could afford one, and I couldn't afford to lose such a sweet job.
Emiratis are guaranteed payment for any education they can attain. They (and we) enjoyed VIP Healthcare 100% covered, and they are given a government house (typically a 5-bedroom villa), or an allowance and plot of land to build their family home when they are married (or special circumstance). They are also given a plot of land for investment (maybe a residential or office tower, etc.). They will lose this for committing crimes.
Because of this, there was virtually no crime, and no need for it. Sure there was likely unreported crimes like domestic abuse, etc., but I mean, I accidentally left my Jeep running, with the top off for an entire day in busy Hamdan Street and nobody dared touch it. I also kept my bike out front day and night. I had a neighbor who was a single mother who did not want to return to the UK because she'd grown accustomed to feeling safe even late at night around even the busiest parts of town.
The remaining crimes are attributable to the unskilled laborer - a terrible institution that you should remove from your scenario, unless you want to have expatriate labor do your jobs for you.
Guns & Weapons: There is some limited firearms for sport and hunting, but because there is strong control of borders, drugs and illegal guns are few and far between.
Equality: While gender equality is very strong and promoted in the UAE, they fall short on homosexuality: it's only legal to be gay if you're a non-muslim and you don't practice it in the country. They also fall very short on the treatment of unskilled laborers and this is manifested culturally as well. But the latter two issues likely won't be a huge issue in the States in 50 years (hopefully). We should be focused on the thinly veiled sexism & racism in our country now - among other things.
Personal equality is done through cultural norm: professional clothing worn by the Emiratis are the same, humble kandora or the modest abaya from the highest sheikh to some guy in Fujeirah. That is until office hours are over and we go to the movies or a bar, then it's back to Western clothing. Weddings have a strict spending limit to avoid extravagence / showing off. Obviously there are ways to get by, driving this-or-that car, giving extravagant gifts to someone when you visit their home, etc.
Violence in Media: Sexuality and violence is censored from film, etc. unless it's artistic. Your America might never show it, but then someone is going to watch a Canadian or Mexican (or whatever) film and you're going to want to censor it.
The other qualifications are inherent, but it should be noted that the censorship of opinion is very strict - although not the most outrageous I've seen (ahem, Russia, Saudi, Qatar, Israel), and because the citizens are kept out of the truth and kept 'fat,' they're very complacent and full, unanimous support for leadership. The country has it's (major) flaws, but for the skilled expatriate and the Emirati, it meets your requirements.
So what would have to happen in the United States?
I'm not saying this is ever going to happen, but for a storyline it might be expanded on...
You have the simultaneous growth of a political party that has the same goals in mind as well as a like-minded media mogul.
Step 1: Get everyone to agree on leadership. This might be easier than you think. I have an aunt that is a Republican because she only listens to those crazy radio stations that use sound-bytes and propagation of lies. The Democrats have these, too, but many, many people get their opinions from main-stream media. Your media mogul buys influence and through censorship gets everybody to love your new politician(s). They amend the constitution, pass legislation, etc.
Step 2: Close the borders and replace migration to guest workers. If someone wants to have a better life and support their family in the United States, because there are better economic opportunities - fine - but they don't get the permanent status that those here enjoy; and there is zero tolerance for any crime. PS- I'm not saying I'm for this. Then close the borders: yes, you will have to post defensive security. PPS- I'm really not for this. Shipments and border crossings are going to be massively controlled - barring the influx of guns and illegal transport of persons. Where will all these guards come from?
Step 3: Ensure everyone who seeks a job gets a high-paying job. This means you even make up entire government agencies and pay people highly; sure you create a lot of lazy people, but they get fat and complacent, because they can buy their nice cars. The competition in the UAE was between which job the Emiratis had - would you rather be stamping passports all day at the border, or would you like to work in the sexy Development department, then you work harder? And to do the real work, there are your guest workers (see step 2) that are paid very well, just not as well as your Americans, and don't want to do anything wrong to lose their job. How do we afford to pay all these fake and real jobs?
Step 4: We have more oil & gas interest per citizen in the United States than the UAE. However, in the UAE, it is largely distributed to provide the benefits that their citizens have, while ours are locked away in ownership and profit by EXXON or whoever. A risky and unpopular claim on the ownership by the new political party is taken, and the profits are given to provide health, education, jobs, & even a home. For every law-abiding citizen.
Step 5: The rest is easy; you have mostly educated and healthy people who want to obey the law, because they so love their leadership and because to lose that would be bad. This is when you further the censorship and keep your tight hold on public opinion, but they're okay with that, because your leadership is flawless, kind, gentle, and generous ... as far as they know.
Step 6: Driverless cars, for God's sake. I'll be happy and sign any social contract for just that: and I mostly bike!
So yes, there are a lot of impossibilities and even unpleasantness in the above, but if you need to achieve something like what you propose, you're going to have to work hard at it :) Happy WorldBuilding!