I have quite a lot of ...

I have quite a lot of experience with grey water treatment, and I agree with many of the comments below.

First issue is what constitutes the grey water.  Does it include kitchen wastewater or not?  Does it include laundry wastewater or not?  The solids - lint, food waste, and FOG will create complexity and require proper removal before you would have any hope with a fixed media bed (sand or otherwise).

I had a lot of success over several years with the following - treatment train:

1. Inclined, curved slotted screen (sieve bend) with additional sprays for periodic cleaning

2. Proprietary circulating bed biofilter, with automatic backwashing sequence based on bed pressure drop

3.  Disinfection by UV and/or Hypochlorite depending on the re-use requirements.

If you want to operate the system successfully in the long term, you need to have elements along the above lines or you will end up with a big mess.

Another huge issue is protecting the microbiological population from the shock of flow/concentration, pH and temperature change, as well as nasty household cleaning materials....

I'm happy to help if I can.

Phil