An ab initio investigation of the family of molecular compounds TM_{2}X is conducted, where TM is either TMTSF or TMTTF and X takes centrosymmetric monovalent anions. By deriving the extended Hubbard-type Hamiltonians from first-principles band calculations and evaluating not only the intermolecular transfer integrals but also the Coulomb parameters, we discuss their material dependence in the unified phase diagram. Furthermore, we apply the many-variable variational Monte Carlo method to accurately determine the symmetry-breaking phase transitions, and show the development of the charge and spin orderings. We show that the material-dependent parameter can be taken as the correlation effect, represented by the value of the screened on-site Coulomb interaction U relative to the intrachain transfer integrals, for the comprehensive understanding of the spin and charge ordering in this system.