Mike,
I don't have any experience with the moving satellite dishes. When we are out with the Murray we are trying to escape everything. We have a 18" flat
screen which I think was used for less than 30 minutes total this past year.
I can tell you that most modern electronic devices use switching power wide voltage power supplies. Most don't care about line frequency or shape as
long as its between ~90 to ~260 volts. Look on the label for the voltage range. They will take modified sine wave just fine.
Devices that use a transformer power supply or devices with motors (like my all electric fridge) only like sine wave power.
Look up the specs on all the devices you plan to install. Add up the devices power requirements ( in watts) to see how much power you will need from
the inverter. All devices have an in-rush current that is much higher when first plugged in, for that reason I suggest doubling the total watts to
select your power inverter. So if your total power is say 300 watts, I would get a 600 watt inverter. If you go way oversize, the larger inverter
will be consuming more standby current.
You should also be aware of the battery size and run time. For 300 watt load @ 12 volts that's 300/12 = 25 amps. The inverter is not 100% efficient,
most are 80-90% so lets pick 80% so the inverter will consume 31 amps. Most people use two 6 volt golf cart batteries which are just over 200amp/hrs,
so lets use 200 amp/hrs. With a lead-acid battery the lower the discharge level the shorter the overall battery life. You should not discharge it
below 50% so that means you have 100Amp Hrs. But the 200Amp/hr rating is at 5C rate (20hrs @10 amps). At 25amps you may have only 150Amp/hrs of
capacity so at 50% that leaves 75Amp/hrs.
So 75Amp/hrs divided by a 31 amp load = 2.4 hours of use. In the real world it will likely be closer to 2 hours. To be really kind to the battery you
should not charge it fast than 5C (20 hours to recharge), but in the real world you can put that charge back in the battery in about 6 hours. You can
charge it faster, but battery life is again reduced.
If you are driving down the road, the engine alternator should keep up with this, although you may want to have it tested and look into installing a
larger engine alternator.
If you are going to use this coach as a stationary party, you may want to look a small generator that is quiet and can handle this small load. It
will not however handle an air-conditioner.
I have an all electric fridge so I am considering go to LiFePO battery. These batteries can be discharged to 80% without harm and can be recharged
much faster. They also weight much less. Progressive Dynamics are now advertising a LiFePO converter charger.
https://en.wikipedia.org/wiki/Lithium_iron_phosphate_battery
Just some thoughts.