Marxism is the original Communism, Marx's writing in a nut shell is of a Utopian society, everyone is equal, none more than another. Plus anarchy, his beliefs were of a stateless society. Ranked 3rd for me.
Marxist-Leninism is Lenin's tweaking of Marxism, which share many of the same principals, but has the idea of a vanguard party, because anarchy never lasts. My number 1.
Trotskyism is again elaboration on Marxist-Leninism, but he preached of the impossibility of "Socialism is one nation", basically having only one Communist country. He also believed in permanent revolution, revolution until the extinction of capitalism. Number 2
I'll group Moaism and Stalinism together as they are basically the same thing. These are what most people think of when they think of Communism. These are the ones that involve secret police, brutal policies, mass murder, restrictions of rights and other fun (sarcasm) stuff. Not even worthy of ranking.
Please we you see "Communism", don't think of Stalinism and Moaism right away, remember the other three, that aren't really that bad.