For simplicity let me work only with connected and simply connected spaces. "Space" will mean a space of this type.
A space is rational if its homotopy groups are rational vector spaces (equivalently, the integral homology groups are rational vector spaces). The rationalization of a space X is a rational space Y and a map $X \to Y$ with induces an isomorphism on homology groups with rational cohomology (a rational equivalence). Rational homotopy theory studies the homotopy theory of rational spaces (and rationalizations of spaces).
There are several equivalent ways to encode the rational homotopy type going back to work of Sullivan and Quillen. For example you can encode the entire rational homotopy type in terms of a commutative dga (Sullivan's rational forms). But this is a lot of structure to carry around, and I am wondering how to encode the rational homotopy type in terms of a smaller amount of data.
Specifically, I would like to know what additional information/structure you need to place on the rational cohomology groups in order to determine the rational homotopy type of a space. I have been told that "Massey products" suffice. But do you really need all Massey products? or can you get away with just some of them? Which ones? I would also be very interested in simple alternatives to Massey products which encode the rational homotopy type.