For the October revolution and early Soviet history, my favourite is Sheila Fitzpatrick. "The Russian Revolution" might be closest to what you are looking for. Also, "Education and Social Mobility in the Soviet Union 1921-1934" is a good social history of early Soviet Union.

As for general history of communism, it depends if you are more interested in actual systems or a history of communism as an idea and political movement.

"The Red Flag" by Priestland somewhat blends the two. It's a large volume, but if you were to read a single book on the later topic of interest that might be the best choice.

A short, clear and concise book on communist, or rather state socialist systems is by Lane, "The Rise & Fall of State Socialism". I like it because it covers both the succeses (early industrialisation, security, degree of equality, etc.), and failures of state socialism (no meaningful political participation, limited freedoms, inability to achieve intensive economic development after extensive one, etc.).

More focused on specific Marxist thinkers and connections between different currents of Marxism and political and social contexts in which they developed is "Marxism after Marx" by McLellan. Similar, but entirely organised around specific Marxists are "Main currents of Marxism" by Kolakovski. However, it is a three volume work, so I'm not sure it would justify time investment for your goals. However, if some specific thinkers peek you interest, you might want to check what Kolakovski has to say about them, and it is perfectly possible to read just bits of that work.

I'm currently reading "How to Change the World: Reflections on Marx and Marxism" by Hobsbawm. First few chapters are an excellent contextualisation and introduction into Marx and Engels, but as yet I can't say anything about later communism in that work as I haven't read those parts yet.