Inconel 625 is a Ni-based superalloy widely used in nuclear and aerospace applications because of its high strength and corrosion resistance. The current paper investigates selective laser melting of Inconel 625 using a wide range of process parameters: four laser powers, five scan speeds, and three hatch spacings. Cube coupons are produced and their end properties are measured, specifically, relative density, surface roughness, microhardness, and surface residual stresses. Process maps are constructed to correlate processing parameters to the part surface integrity, and the possible underlying causes are highlighted. Experimental results show that highly dense parts can be produced using selective laser melting and low average surface roughness can be obtained in both the scan and hatch directions. Hatch spacing is the most prominent factor to attain relative densities above 99% while high laser powers are key to lower the average surface roughness. Microhardness and microstructure examination are done for a subset of the process parameters and found to not significantly change with laser power. Surface residual stresses are measured on the top surface in the scan and hatch directions and process maps are developed. There is no particular parameter that solely affects surface residual stresses, despite several cases where the increase in laser power reduced the surface residual stresses. 90% of measurements showed surface tensile residual stresses except for a few cases that resulted in surface compressive residual stress.