I think you get one or the other. I do not keep a generator on my rig so the battery model was best for me. I believe I have a shur-flo on demand 2.8gpm pump. It's connected to my battery via a toggle switch.
I have a gated wye after the pump, one goes to washer and one to garden hose.
I plan to add a gated wye immediately after the tank as well. One will go to the pump, the other will be plumbed to allow me to fill buckets/bottles without pressure, and to connect a garden hose and fill my tank without the hassle of holding the hose in it. Without this set up, it's very difficult to fill bottles because you get a constant pressure that tends to blow water and product out of small containers.
As far as which power washer, there's a lot of variables there. I chose the Landa commercial gas power washer for a few reasons. It's gas, so I don't need power if doing a wash. It's also commercial grade with a warranty. Home owner models aren't made to run a lot, and will fail prematurely if overused. But the price for mine was 850, which was the cheapest commercial washer in their line, so it's a cost/benefit thing. 2 years warranty on engine, and 7 years on pump. Or possibly vice-versa. Either way, its anticipated to last me longer than several homeowner models with how often I use it.