The PHQ has many uses.
First as a Player Headquarters, where you can dock all your ships safely.
It docks 8 capital ships, 16 freighters/M6 size, and a unlimited amount of fighters.
It becomes an ideal place to send capped ships to wait for you to want to do anything with them. It repairs ships if you give it resources.
It will reverse engineer any ship in the game and allow you to build it. And it has a spray shop if you want to give your ships all the same colour scheme.
But it is also useful as a Superstore. It has a single large cargo bay, with no restrictions on how much of anything can be stored there. As such, this is a perfect place to store all the stuff you slurp up. At average price minus 1, all the basic stuff will sell itself. It’s a good place to put any oversupply of secondary resources from your complexes. Some stuff wont sell from there, but that is good because it makes a great place to store all the stuff you don’t want to sell, and do not want to have to carry around in a ship.
WARNING: I found out unfourtunatly that if you use it to store stuff turn off the NPC trading option as soon as possible. I ended up hunting down all the traders that took my PSP and other hard to get items.