There is no 'right' order in which to install components but, as a general rule, it's more convenient to install the "flattest" - ie those which sit closest to the board - first. This allows the board to sit flat on the workbench when you turn it over to solder and prevents the component from dropping out before it's soldered.
The remaining unused holes in the board shown here are for the wires which connect to the various sockets mounted on the case. Once the board is fitted into the case, it won't be possible to solder these wires, so they need to be soldered in next. However, it's better to make a start on the case now so that the required lengths of these wires can be judged.