Before I forget, great picture. Came out really looking great!
I can share my own experiences with you using a 4 KW Powermate (5 KW Surge). My initial experiences were with that Powermate. I initially bought it when my wife's mom was alive and 100% bedridden. More and more support equipment was moving in as she became worse. I went with the 4 KW unit as I wanted a generator with 240 VAC out to make connecting to the house mains easy. Even though it was a manual process, I needed to make the change over simple so the wife, her brother or her older dad could do the task.
That little unit did fine and would run the gas forced air furnace blower motor, all basic lighting and appliances including two refridgerators and a large freezer. Consider that refridgerators, freezers and a furnace only run on demand and with any luck won't all demand power at the same time. As long as during a power outage users don't needlessy open refridgerator doors they don't really cycle much at all. When the furnace blower motor would kick on there was a slight drop in RPM the instant the load was applied but that dip was very quick and hurt nothing.
Looking at the generator output on a scope really isn't too revealing. Figure a 120 VAC RMS sine wave will yield a 340 Volt Pk to Pk sine wave you really won't see much low level noise or distortion riding on the peaks and valleys. To get fancy you need a good power analyzer and I never bothered.
You could go from item to item and add up the individual power demands for a rough idea of everything he wants running.
If I had it to do again I would have gotten a unit with a larger fuel tank. I think it has a 1.5 US Gallon tank and during long outages required fueling more than I liked. I was going to get a larger tank but the wife's mom passed away so I never bothered.
The then TV ran fine on it, it was an old big screen Magnavox.
Today it has all been replaced with a natural gas unit and full automatic transfer. Everything I have concerns with has UPS backup including the new TV a large flat panel Sony. The TV even runs fine on the UPS which produces an ugly modified square wave. The UPS units only need to support their loads for about 8 seconds as within 10 seconds transfer to the new generator happens.
Overall those little Powermates do a good job. The old 4 KW unit sits in our shed and that unit has helped neighbors countless times during outages. Looking back I bet I got that thing 15 years ago.
Ron