I use an APC Smart UPS with supposed sine wave output. Here is a very quick and dirty video of me running my SO3 and just yanking the power cord out of the wall.
Run time just depends on battery capacity and workload. You could get a Kill-A-Watt or something similar to see what the running load of your whole system is. Then you can determine what battery capacity and load you need based on how long you’d like it to run your whole system.