A very simple circuit is add an RC time delay to the V+ input of each circuit, each delay greater that the previous one in the series. This is efficient only if each subcircuit doesn't draw much power, otherwise consider the series resistor wastes energy. On power up:
1234
but on power down its
1234 too.
When power is applied, the capacitor will appear as a short to ground and ramp up. By using different RC combos on each circuit, you can either calculate it or just wing it, you can delay power up by a defined amount; low tech and parts count, easy to implement.
However, on power down, the last item to power up is also the last to power down because it has the largest capacitor in the sequence.
To shut down in reverse order you need to design a switching circuit, or quickly and dirty, a multi-pole mechanical switch. When the circuit is switched off, each pole of the switch should short smaller value resistors to ground to reduce the series resistor in V+ of each subcircuit, so it discharges the capacitors at a faster rate, choose the values so the time constants for 4,3,2, are reduced for the right sequence.
You can do the above in silicone too and use the AD chip, its more compact and precise.
All those added caps also debounce mechanical switches for you, and you can add a sufficient large cap across the main power supply to compensate for the switches momentary disconnect, if that is an issue.