Optimal laser irradiation conditions for water-window (WW) x-ray emission (2.3-4.4nm) from an Au plasma are investigated to develop a laboratory-scale WW x-ray source. A minimum Au target thickness of 1 µm is obtained for a laser intensity of ∼10^{13} W/cm^{2} by observing the intensity drop in the WW spectra. Au targets produced by thermal evaporation are found to have a higher conversion efficiency than commercial foil targets for WW x-ray radiation. In addition, optimal laser spots for fixed laser energies (240 and 650mJ) are found for an Au target ∼1mm in front of the focal point, where suitable conditions for plasma temperature and plume volume coupling are achieved. The mechanism of the optimal target thickness and spot size can be well explained using a radiation hydrodynamic simulation code.