I want to outline a skeleton programme for a "dictatorship of the proletariat". It's important to understand, though, that if there were a communist revolution, and the power and privilege of the capitalist class were decisively broken, at least temporarily, the actual programme immediately following must and should be a matter of politics, i.e. negotiation and compromise (with some propaganda thrown in). What follows is just a collection of ideas, not a system of government I think a successful revolutionary force should impose in toto following a revolution without regard to the specific opinions and preferences of those with some social and political credibility.
It's also important to remember that the governments immediately following the Russian and Chinese revolutions faced a severe theoretical problem: the actual industrial proletariat in those societies was a minority, overwhelmed numerically by a class seen only in primitive feudal societies: the mostly illiterate agricultural peasant class. Agricultural peasants have a very different economic relation to the feudal landowners than industrial workers have to the owners of capital. Canonical Marxist theory (i.e. the theories that Marx and Engels themselves proposed) depended not just on the industrial proletariat forming a numerical majority, but also on specific features of the industrial proletariat and their relation to the capitalist class. Most of the pre-Lenin communist, socialist and anarchist theoreticians were, after all, living in the rapidly industrializing Western Europe.
Lacking this majority, and starting from the majority with an entirely distinct set of economic relations between peasant and landowners, the Russians and Chinese revolutionaries faced enormous uncharted theoretical ground. And they did so under the enormous pressure of life-and-death expediency faced by rulers of countries not just faced by primitive on-the-verge-of-starvation productive forces but also countries under the pressure of severe international hostility. The nascent Soviet Union started out with a primitive agrarian economy; what little industry they had was mostly colonial-submissive and administered by its foreign owners or those specifically chosen for their submission to those foreign owners. And then this primitive economy and its labor force was shattered by the First Imperialist War. Lenin inherited a country in shambles. And then they had to overcome a civil war and blockade fomented and encouraged by the capitalist West, knew that a Second Imperialist War was in the works (it's arguable that the West's hesitancy in confronting Hitler was in no small part due to Hitler's hostility to the Bolsheviks), and even afterward knew that there was substantial support for a Western invasion of the Soviet Union.
Similarly, forty years later Mao Zedong had to take seriously the profound existential threat of a nuclear-armed Soviet Union already leaning away from internationalizing socialism and toward its own brand of imperialist hegemony. And of course revolutionary China escaped actual nuclear war with the United States only by the narrowest of margins: MacArthur actually had nuclear weapons (granted to him by the Joint Chiefs of Staff) with the explicit intent of using them on China when Truman successfully faced down what was a de facto military coup. if Dewey had won the election, if Truman didn't have (if you'll excuse the gendered metaphor) balls of steel, if MacArthur hadn't backed down, things might have turned out very differently.
I've had a gun pointed at me, and I know you do whatever you have to do at the moment to survive. I can't really judge the behavior of a government that has nuclear weapons pointed at their country.
Regardless of the specific conditions that might obtain immediately after a communist revolution, we don't face these conditions in the United States. We will not face the predominance of an illiterate peasant class and their economic relations to a feudal land-owning class. We will not start from a barely subsistence-level economic infrastructure. While we might have to deal with some destruction of infrastructure caused by civil conflict, we won't have to face the devastation of an international war against a determined and industrialized enemy. We will probably not face an existential threat from the remaining nuclear powers: China, the European Union, India/Pakistan, and possibly a Brazilian dominated South America. We will have considerably more freedom and luxury to experiment, as well as to tolerate temporary inefficiency.
There are only two conditions that historically have led to an internal revolution. First, some class by virtue of its socially constructed characteristics achieves substantial economic power unavailable to the contemporaneous ruling class, and resists and overthrows the ruling class from a position of strength. These conditions allowed the nascent merchant and industrial-owning "middle" classes to overthrow the feudal ruling class. Second, the ruling class completely self-destructs, and whoever happens to be the most organized at the time has the reins of power thrust into their hands. These conditions placed power in the hands of the Russian Bolsheviks and Mao's Chinese Communist Party. (To a certain extent, the Chinese Revolution was a mixture of the two conditions: Mao had gained at least some economic power before the revolution by organizing and governing areas in China's interior.)
In all probability, the conditions that would obtain for a communist revolution in the United States would, regrettably, be the latter. (Although, like Mao, it is possible for communists to create some sort of economic base before a revolution.) This means that while a communist revolution would not be starting with a fundamentally subsistence-level economy, they probably will be starting with an catastrophic economic conditions that will be causing profound suffering, starvation and disease, and that will require immediate measures to correct. They will inherit quite a few pervasive social and economic conditions favorable to increased production; they will have some luxury for experiment and inefficiency, but the devastation will limit these options. It is with these historical observations and imaginative conditions that I'll be outlining a proposed skeleton programme for a post-revolutionary communist government.