I am not a fan of leasing so have not looked into that company. When looking at batteries you need to look at the power/energy and compare it to what you need. Power would be peak kW it can run at. If your power peaks at 3kW to run tank/fridge/internet and that is all you want, you need a battery system rated higher than 3kW. If you want to run your a.c. you need a battery system that handles the running draw as well as the startup surge. Then if you want to run your 3kW of load for 10 hours, you need 30kWh of battery storage, plus a few % for efficiency losses.
There are also portable battery systems that can be charged from a generator. Benefit of having both is that you can get a smaller battery that is just enough to last the night and only have to run the generator at full load for a few hours a day to charge it back up. Solves the issues of having to keep an eye on the generator to top it off, make sure no fire, pissing off neighbors due to non stop noise, and advertising to desperate passers-by that you have what they need in the middle of the night when you are likely asleep.