I finally put together my battery box. I settled on a 22 inch Husky toolbox. It was a little larger than I wanted, but seemed like the best compromise. At the moment it houses one 36 Ah Lithium iron phosphate battery, which is wonderful. It is pricey, but only weights just shy of 5 lbs and can be recharged up to 2000 times. Very little voltage drop until the end. To judge how much power I might have left, I went for a "Watts up" which shows voltage, current power consumption and total used energy (in Ah and other units - one of the attached pictures shows my phone plugged into the USB port).
I put in a main power switch, a separate voltmeter (got that before I got the Wattsup), 2 lighter sockets (each attached to a resettable 10A fuse) and one double USB port to keep my iPad/phone alive.
All ports and switches are in a recessed compartment in the lid. There is enough room in the box to easily add two more batteries (not that I want to spend that much money - but who knows in the future).
I wanted this to be multifunctional, not only for astronomy.