Your question is a complex ones as Marxist theory has been re-interpreted a number of times to suit the needs of the user. Marx based much of his work on earlier philosophers, such as those writing about the French revolution, and did not always complete his thoughts or left some ideas ambiguous. What sets his philosophy apart from others was his focus on class struggle as a means to an end, but even that wasn't 100% clear from his writing:

"If one reads The Communist Manifesto carefully one discovers inconsistencies that indicate that Marx had not reconciled the concepts of catastrophic and of permanent revolution. Moreover, Marx never analyzed classes as specific groups of people opposing other groups of people. Depending on the writings and the periods, the number of classes varies; and unfortunately the pen fell from Marx’s hand at the moment when, in Das Kapital (vol. 3), he was about to take up the question. Reading Das Kapital, one is furthermore left with an ambiguous impression with regard to the destruction of capitalism: will it be the result of the “general crisis” that Marx expects, or of the action of the conscious proletariat, or of both at once?" From Source

And so, other leaders have taken his work and expanded on it or selectively used his words to meet their own ends, this is where we get the Leninist and Maoist 'versions' of Marxism. We have to remember as well that Marx was not defining communism here, merely explaining the reasons for and the possible methods of revolution: "However Marx refused to speculate in detail about the nature of communism, arguing that it would arise through historical processes, and was not the realisation of a pre-determined moral ideal. " Source

So in reality, if a country achieved a more communal state through class struggle, they are Marxist. The resulting system is not as important as the method, merely looking at it from a Marxist point of view. In this regard, both the USSR and China are Marxist, because both underwent class struggle to achieve their new society - the Bolsheviks fought the Russian monarchy and the Mensheviks, and the CCP fought the Nationalists under Chiang Kai Shek, who had been integral in overthrowing the Chinese Imperial line.

But what makes a country communist? Because we don't even have a clear definition of what communism is, that really depends on who you are talking to. A purist might say any society in which there is common ownership and no government is a communist state (so, they dont currently exist), but a Marxist might say that even a state with a government and wages would count since Marx identified two stages to the transition ("the first would be a transitional system in which the working class would control the government and economy yet still find it necessary to pay people according to how long, hard, or well they worked, and the second would be fully realized communism—a society without class divisions or government, in which the production and distribution of goods would be based upon the principle" Source) and so a society could still be in stage one but consider themselves communist since they are working to achieve stage two. If they were to achieve stage one, it would be more in line with a purist way of thinking, which didnt/doesnt exist considering there have always been people in positions of power (Stalin, Mao, Kim Il Sung, etc.).

So you can, call the USSR and China and other nations that have attempted a revolution as communist, but you'll have people fighting with you no matter what because in their opinion, they have not completed the revolution, and thus are not examples of 'perfect' or 'true' communism. This where you get into the argument about human nature and whether or not we even CAN live in a society not beholden to reward systems, but thats a whole other can of worms.

As for completely unbiased sources, your best option is exploring Russian Revolution and Cold War historians like John Lewis Gaddis who use resources from multiple view points to help understand the how and the why. Trying to strictly read about communism gets you into some dubious places as you said, and as I pointed out we don't really have a great definition beyond 'classless, governmentless, ownershipless society', so the best way to learn about the people who consider themselves as communists is to see them in a larger perspective, comparing them to better understood entities like capitalist USA, or to other communists, like Stalin and Trotsky.

Side note: This issue with not understanding what communism even is shows constantly, when people call socialist countries communists for example. Socialism is differentiated with it's lack of violent revolution - you can think of it as the US and Canada and how they broke away from the UK. The US won independence from the UK through war (violent revolution, like communism), but Canada won it peacefully by pretty much asking for it (non-violent revolution, like socialism). And even then, there are no truly socialist countries, only countries which use socialist programs, like Canada. It really doesnt help that people like McCarthy made the US so paranoid about communists that it's meaning has become twisted and entirely inaccurate in some cases, to the point where it has lost its original meaning.