That's the problem - their real needs are not clear.
On hook-ups a single battery will do, no battery will do as well.
Without hook-ups - too many variables, but I would still prefer more than a single battery. 2*6V or 2*12V (or 3*12V if it fits). Doesn't have to be Lifeline Concorde, but the size (of the total battery bank) matters.
It is possible to stay up to 3 days with a single battery and without a generator or solar if you don't run furnace and high-current items like MW, toaster, hair drier etc. Fridge would account for most of energy consumption then. Many people would call this a "survival mode" and would tell you that this is beneath your dignity, and now that you've spent $$$ on a trailer you have to spend another several hundred (or a few thousand) on other equipment :). Tastes differ.
In case of a single battery I would prefer it as big as practically possible. Batteries are heavy, it is easier to handle 2*100AH @12V than 1*120AH @12V. In other words - there is very little reason to go for a single battery (without hook-ups).
I would also get some solar before the generator - it is cheaper, and it will be useful even if you decide to carry a generator because generator alone will not get you a proper charging unless you run it day and night. With only lights, pumps, radio, occasionally furnace, occasionally small electronics, no high-current items, AND if it is sunny enough, a portable 100W solar ~$300 will keep you afloat for long time. I am not a big fan of portables and think they are way too expensive for what they deliver, but this is an easy way to start for those who are not sure.
You will figure out your needs as you go.