I had an underfloor battery for a Car Radio in my lounge. Works if mains has gone for about a week. The charger I used was a Halfords one so why not just go the same way? I had mine on a timer to charge for 1 hour once per day.
Hard one! As a computer uses different power at different times. You would need to know what average power is being consumed (Wattage) by the computer being used, remembering also the inverter also consumes power, even when idle & connected to the battery. Most computers use around a 100/150 watt unless you go for something like the fit PC @ around 10watt.
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