Appreciate your comments, ideas 4 equipment in tiny trailer

We have been slowly getting material for a modified tiny trailer based on Steve's Puffin. We want the ability to "boondock", so need a generator, deep-cycle battery. and of course, propane. We are looking at the honda eu2000u from Wise delivered to my door for $869. The battery would probably come from walmart - any recommendations? We have on hand the fantastic power vent, and would add an extra vent for the "bathroom" and the kitchen counter area. We want a small air conditioier similar to Steve's that the generator would work well with. We have a small 110 heater.
Steve's idea of the shower with the sprayer outfit is simple but very efficient it seems. The porti potti under the counter that slides out facing the exit door helps save space (the counter runs the full length of the front wall). The bathroom can be curtained off when needed.
We would want to wire the trailer for use with battery, the generator, or at a regular campground 110 system.
Thanks for your input.
Steve's idea of the shower with the sprayer outfit is simple but very efficient it seems. The porti potti under the counter that slides out facing the exit door helps save space (the counter runs the full length of the front wall). The bathroom can be curtained off when needed.
We would want to wire the trailer for use with battery, the generator, or at a regular campground 110 system.
Thanks for your input.