Properties of various core-shell silicon nanowires are investigated by extensive first-principles calculations on the geometric optimization as well as electronic band structures of the nanowires by using pseudopotential plane-wave method based on the density-functional theory. We show that different geometrical structures of silicon nanowires with various core compositions, formed by stacking of atomic polygons with pentagonal or hexagonal cross sections perpendicular to the wire axis, can be stabilized by doping with various types of semiconductor ͑Si, Ge͒, nonmetal ͑C͒, simple metal ͑Al͒, and transition metal ͑TM͒, 3d ͑Ti, Cr, Fe, Co, Ni, Cu͒, 4d ͑Nb, Mo, Pd, Ag͒, and 5d ͑Ta, W, Pt, Au͒, core atoms. Dopant atoms are fastened to a linear chain perpendicular to the planes of Si-shell atoms and are located through the center of planes. According to the stability and energetics analysis of core-shell Si nanowires, the eclipsed pentagonal and hexagonal structures are energetically more stable than the staggered ones. Electronic band structure calculations show that the pentagonal and hexagonal Si-shell nanowires doped with various different types of core atoms exhibit metallic behavior. Magnetic ground state is checked by means of spin-polarized calculations for all of the wire structures. The eclipsed hexagonal structure of Si-shell nanowire doped with Fe atom at the core has highest local magnetic moment among the magnetic wire structures. Electronic properties based on band structures of Si-shell nanowires with different dopant elements are discussed to provide guidance to experimental efforts for silicon-based spintronic devices and other nanoelectronic applications.