The Communist Manifesto details the natural rights of everyone to equality and shared prosperity.

I read it a long time ago, but my memory is that the Manifesto (and its writers in general) discard the idea of 'natural' rights, arguing that legal / moral principles arise from the economic conditions of the time.

Marxist Communism is a bit myopic as it really deals with factory work

Marx's biggest scientific contribution is the development of a 'materialist' (here meaning 'physical') theory of history. I feel that his specific stages are too eurocentric, but the general principles are universal.

The Manifesto is a call to action, so it is somewhat simplified theoretically and deals specifically with the issues and conditions of the time.