A generic scheme for the parameterization of mixed-state systems is introduced. A slightly modified version specially for bipartite systems is then given, and especially applied to a two-qubit system. Various features of two-qubit entanglement are analyzed based on the scheme. Our formulation of the parameterization and the analysis of entanglement properties exploit the interplay between pure states as Hilbert space vectors and pure as well as mixed states as density matrices. Explicit entanglement results are presented, in terms of negativity and concurrence, for all two-qubit mixed states with one single parameter/coordinate among the full set of fifteen being zero and a few other interesting cases.