Hi Dave and welcome to Permies!
You don't say where you are located (location, soil type, climate, etc), but if you are using that small amount of water, you could just directly put it into the landscape without a filter - sand or otherwise. I have used an outdoor shower since 2008 and have also dumped my dishwater into the landscape from plastic tubs for about the same amount of time. Basically both greywater sources go into infiltration pits covered with woodchips that act as a biofilter and build soil fertility.
You can see my shower setup here:
Part 1 and
Part 2
I haven't written a blog yet about my new KRD (kitchen Resource Drain) yet but here are a couple of pics of the installation of the new infiltration basin. Basically I decided to do this because of pain issues caused by a chronic autoimmune disease - it was becoming an issue in lugging the water outside all the time. Now I don't have to!