How would I delay a power on and power off
I would use a timer (555) or small microcontroller (Attiny85) for sequencing the power. In fact, I do exactly this for one of my robots.
Tie the source of the MOSFET to the gate of the MOSFET with a pull-up (4.7 kOhm is good) and tie a signal-level N-channel MOSFET like the BS170 to pull that gate down (thus turning on the P-channel) when given signal from the Attiny.







simulate this circuit &ndash; Schematic created using CircuitLab

You can use the ATtiny to sequence power however you want.