Of the infinitude of academic distinctions of Marx's writing to be raised here, the distinction between "political Marxism" and "analytical Marxism" seems fruitful. For the purposes of this distinction, political Marxism would be the set of writings embedded in the political climate of Marx's age, The Manifesto, etc. The politics that resulted from these writings bloomed initially, but as the mantle was passed through Stalin, Lenin, Trotsky the politics became increasingly fraught with problems (being gentle here.)
Analytical Marxism for me is limited to _Capital_. Marx proceeds analytically, taking the rich tradition of political economy to heart. Ricardo and Adam Smith are addressed directly. Marx attempts no emotional arguments here, no appeals for solidarity or revolution. Instead, the ideals of capitalism (e.g. exchanges between individuals are mutually beneficial) are taken as true, and Marx attempts to create a framework for analyzing the structural forces that result from this economic mode.
_Capital_ provides a set of analytical tools that are timeless and non-dogmatic. A great example is the exploration of how the relative prices of various commodities are set (Marx suggests it is emergent behavior). _Capital_ also takes on such problems such as the contradiction between exchange value and use value, and how the investor's and producer's perspective on exchanging commodities and money differs. These are problems many writers wave away as non-problems by maintaining a myopic focus on individual exchanges.
_Capital Vol.1_ Text http://www.marxists.org/archive/marx/works/1867-c1/ A crash course youtube of Marxist analysis http://www.youtube.com/watch?v=qOP2V_np2c0 All of David Harvey's supplemental materials to _Capital_ are highly recommended: http://davidharvey.org/reading-capital/
Another text you might be particularly interested in is _The Making of the English Working Class_ by E.P. Thompson, which expounds a humanist perspective on the migration from farm to factory in England.