The only word here with a consistent definition is anarchy. The rest are anti-concepts.

read Marx, then branch off into whatever ideology sounds interesting. I personally am a council com, but a lot of people don't like that. But if you're interested, Workers Councils (1947) is a good place to start and Marxists.org has just about every Marxist text there is. But a simple definition of communism, is a stateless,classless,moneyless society in which the workers have democratic control over the workplace (abolishing private property) this, however, does not mean PERSONAL property, as Marx specifies bourgeois property. 

I tried to summarise as much as I could. I really hope you find this helpful 

Capitalism:

Capitalism is an economic and social system based on the private ownership of the means of production, the pursuit of profit, capital accumulation, and wage labor.

Socialism:

Socialism is a political and economic ideology that seeks social equality through the social ownership of the means of production, aiming to overcome capitalism.

It is considered a transitional phase between capitalism and communism.

Communism:

Communism is a political, social, and economic ideology that aims to establish an egalitarian society, without social classes, without private ownership of the means of production, and without a state. Based on Marxism, it proposes that production be geared towards human needs.

Anarchy:

Anarchy is a sociopolitical concept that advocates the absence of governmental leadership, imposed hierarchies, and state domination, focusing on individual freedom and voluntary organization. 

Note: I heavily recommend you read books like the Communist Manifesto by Marx and Engels, and you could always read Pierre-Joseph Proudhon (first anarchist philosopher) and Mikhail Bakunin (also anarchist, Marx's rival).