I'm not entirely sure what the OP is asking for.
"Anti-state" communism can be applied to any form of libertarian socialism, I think. And it seems most relevant to then talk about what anarcho-communist texts you ought to read. Pretty much the main one you need to read to understand what anarcho-communism is would be Kropotkin's Conquest of Bread. Other than that, there aren't really any "basic" anti-state communist texts, since "communism" has otherwise predominately been associated with Marxism, and Marxism has predominately been authoritarian. There are a variety of strains of libertarian Marxism, but they all are Marxist nonetheless, so in that case "the basics" would first be Marx if you haven't already read him. The first book of Capital should be enough IMO for getting the idea about what Marxist political economy is (he just goes on and on and on and on...), and then other than that it really depends on what strain of libertarian Marxism interests you. But you could just as well read Fredy Perlman's (a libertarian communist himself at the time of writing this) "The Reproduction of Daily Life". In fact I would lean towards recommending that over Marx.
The Situationists and the Autonomists are probably the most influential libertarian Marxists, so I would at least read them.