  The iron pnictide and chalcogenide compounds are a subject of intensive
investigations due to their high temperature superconductivity.\cite{a-LaFeAsO}
They all share the same structure, but there is significant variation in their
physical properties, such as magnetic ordered moments, effective masses,
superconducting gaps and T$_c$. Many theoretical techniques have been applied
to individual compounds but no consistent description of the trends is
available \cite{np-review}. We carry out a comparative theoretical study of a
large number of iron-based compounds in both their magnetic and paramagnetic
states. We show that the nature of both states is well described by our method
and the trends in all the calculated physical properties such as the ordered
moments, effective masses and Fermi surfaces are in good agreement with
experiments across the compounds. The variation of these properties can be
traced to variations in the key structural parameters, rather than changes in
the screening of the Coulomb interactions. Our results provide a natural
explanation of the strongly Fermi surface dependent superconducting gaps
observed in experiments\cite{Ding}. We propose a specific optimization of the
crystal structure to look for higher T$_c$ superconductors.
