You'd do really well to get
Art Ludwig's book,
Create an Oasis with Greywater.
His
website also has a huge amount of information.
I learned a huge amount from this book and I'll be pulling it off the shelf and rereading sections for years. If you're considering any type of greywater system,
Art Ludwig seems to have seen that type of system be installed, and how it works or fails.
I have two ideas related to your question (based on the book, which i can't recommend highly
enough):
1) Any kind of greywater system that involves pumps and/or filters is likely to keep requiring maintenance. If you are not mechanical or you don't like pulling hair out of a stinky gooey pump on a regular basis, you may want to avoid those systems. Ludwig points out that the organisms in topsoil or mulch are great at purifying greywater, while providing water to plants.
2) Before installing your greywater system, ask yourself what your needs and motivations are. If you really will be in places that have no other source of potable water (middle of the Sahara, perhaps? The Space Station?) then the expense of installation and maintenance would be worth it. But if you are in the US you can probably get other potable water much more easily. The filtration unit you're imagining might turn out to be more bulk to carry in your RV than to occasionally carry water tanks in the RV when you happen to be going to places with no potable water nearby.
There are lots of small and simple camping water filters that will make slightly dodgy but clear-looking water safe, if you camp near a stream, for example.