We ran PEX pipe from the fresh water tank to the on-demand hot water heater, then to all units needing water - shower valve, kitchen sink and bathroom sink. It's all run above the ground in hopes to be able to use it in colder weather, as not to have the pipes freeze. The material expands so it's supposed to prevent cracks in case the system does freeze, it's a much more modern plumbing system than what the original trailer was supplied with.
In choosing a shower system, we had a lot of details to consider. We put quite a bit of thought into whether or not we wanted a handheld unit, and whether that would be the sole shower head. Ultimately, due to the small area, we decided to do a rain shower head, so that all the water would be directed straight down into the pan. However, we loved the idea of being able to easily clean the shower, and the handheld piece would also allow us to use slightly less water while on the road.
We purchased both the kitchen and bathroom faucets from Home Depot, and the shower fixture is a Moen from Amazon.