Ab initio molecular dynamics simulation is used to study the structure and electronic properties of the liquid Ga-Se system at the three compositions Ga$_2$Se, GaSe and Ga$_2$Se$_3$, and of the GaSe and Ga$_2$Se$_3$ crystals. The calculated equilibrium structure of GaSe crystal agrees well with available experimental data. The neutron-weighted liquid structure factors calculated from the simulations are in reasonable agreement with recent neutron diffraction measurements. Simulation results for the partial radial distribution functions show that the liquid structure is closely related to that of the crystals. A close similarity between solid and liquid is also found for the electronic density of states and charge density. The calculated electronic conductivity decreases strongly with increasing Se content, in accord with experimental measurements.