Uh. Union of Soviet Socialist Republics, not communist republics.
My knowledge of Soviet history is incomplete, but surely you're not suggesting that the USSR didn't claim to implement communism.
Oh, and hey: many people do claim that the USSR wasn't actually _socialist_. You'll find two groups who do this: anarchists, and new Marxists who still have some liberal left in them. The USSR certainly claimed to be socialist, and was according to socialist principles.
The two groups will make this incorrect, revisionist claim because of two reasons. Anarchists want to bolster socialism while trashing statism, so they want to play up 'state socialism's failures. New Marxists will want to play down any perceived 'failures' of Marxism by distancing themselves from said 'failures.'
If you only want one book, that book is Capital I. I suggest David Harvey's lectures along with it, they'll help out quite a bit. If you have read Smith and Ricardo, that'll make it much easier, too. For bonus points, read the short "Wages, price, and profit" by Marx, it's a bit easier of an intro than the book's.
If you can fit in a second, I'd suggest "the State and Revolution" by Lenin.
Marx identifies a problem and a crude solution, and Lenin provides a good solution. Those two will give you the most of it. Wikipedia, especially on the historical/dialectical materialism stuff, is helpful.
A more full list is here: http://www.reddit.com/r/communism/comments/wisiw/basic_marxi...
Also, /r/communism101 is very good and there to answer questions, if you Reddit.
I'm aware that the USSR didn't implement pure Marxism, but implemented something called "communism" and invoked Marx as its deity. I think that a purely classless society as Marx envisioned is probably unachievable. I really am trying to avoid equating support BI with some ridiculous 1950s idea of Soviet communism, and I'm probably doing a pretty crappy job of it.
All that said, the whole concept seems to me to lead down a path that drives entrepreneurs out of the market by making the cost of doing business greater than the profit of it, which would necessarily lead to the nationalization of industries deemed essential. A society in which private entrepreneurs are taxed to a point of zero net revenue is effectively indistinguishable from the state's name being on the deed. I recognize that that the concept of that level of taxation is severe, but I'm also trying to figure out why it wouldn't eventually happen.
As simply as I can state it, BI seems flawed to me because the cost of living is pegged to the cost of goods, and the cost of goods in a competitive market doesn't have a lot of downwards elasticity. The funding for BI would have to come from producers, which would drive up the cost of those goods, which would drive people out of the market, which would reduce competition and increase the cost of goods, all of which increases the minimum BI necessary to achieve a consistent quality of life. That seems to be to be a feedback loop of which the end effect is the effective nationalization of business in order to control prices.
Many people obviously disagree that that's the end result. Experience would tell me that I've made an assumption that they haven't, and I'd like to figure out what that assumption is, and how viable that assumption is.