What concepts in general chemistry are especially important to learn, in preparation for biochemistry?

You should be good at quantitatve chemistry absolutely

This deals with calculating masses, volumes, concentrations and how to determine these from two sides of a chemical equation/reaction.

Other topics you learn in general chemistry are the basics of the atom:  protons, neutrons, electrons...electrons in atomic orbitals (electronic configuration)...an introduction to quantum numbers related with electron uniqueness.  Chemistry is all about the movement of electrons after all.

Later you are given theory of the formation of molecular orbitals and of coordination chemistry and ligand geometries.

Once you complete general chemistry (typically inorganic), you then learn organic chemistry (the chemistry of carbon).

Then you are ready to learn biochemistry, the chemistry (and biology) of biologically important molecules as metabolites of pathways important in life.