How many amp-hours?

Hi! I would like your opinions. I have an ATC Panther (pop-up TC) that we are building out. The TC came with a 79 amp-hr battery, which we found to be insufficient. So what does our rig warrant in terms of amp-hrs?

We run ...
-- Dometic electric fridge (0.81 Ah)
-- Fantastic Fan 1.8Ah (but only on a few hours)
-- DIY swamp cooler (unknown, but will be on all night)
-- Recharging electronics, like phone, watch, Kindle, camera battery using an inverter (unknown)
-- 2 indoor LED and one outdoor porch lights
-- And we may want to add some other electronics like a Mr Heater Boss Shower, but not sure exactly what or when, so I want to over-estimate my need at this point.

Before we had solar panels and only had the fridge and lights, we would get down to a 60% charge after a day and charge by driving the truck (alternator).

So we added three 100 watt solar panels, thinking if we were camped under some trees, we might still generate enough to make a dent. And we camp (no hookups) in the winter. And there are some days we get little sunshine.

So with all that, I was thinking a 200Ah deep cycle battery. Too much? What are your thoughts?