Get a digital voltmeter mounted somewhere convenient. Be sure the voltage is always above 12 volts. Some people will go lower but that's my basic rule. An led tv will use less power than lcd. My 40" vizio pulls about 5.5 amps and I power it off a Xantrex prowatt 600 with remote pendant. The inverter pulls less than 1/2 an amp if I recall. You can find that info about the inverter in their specifications. You want to mount the inverter close to the battery with large enough cables. You can isolate the 120 circuits that you want power on such as the bed room or living room where you will have televisions. You want to run as many of your gadgets straight off 12 volts vs inverting. Some power is lost during the inversion process.
When and how much you run the generator is part of your energy management plan. Without a monitor to tell you how many amp hours you used overnight you will have to go by your voltage. You can run your generator in the morning to charge and run the heavy morning appliances like microwave, coffee pot and hair dryers. You may also do an afternoon or evening charge while making dinner.
As you get the hang of how much power you are using vs your battery voltage you will develop an idea of how much generator time you will need. Keep an eye on your water levels. The more you push them up and down, the more water they may use. You also need to look at your converter voltage. If it's only 13.6 you will be listening to the generator a lot.