My 200-Watt solar kit included a solar controller which tells current battery charge, amps coming in, and volts. I also have a remote controller for the inverter that tells me state of the battery while the inverter is in use. The setup is not a true battery monitor however. I can't tell how many amp-hours any particular device uses, but I can tell if the batteries are getting low and get a good estimate of how fast they are draining.
I do not have my inverter connected to the house circuit. I use the outlets on the inverter to power whatever device I want to use, and typically for fairly short durations. I've never tried running a TV off of the inverter. I primarily use mine to power a small ice maker, slow cooker, or the occasional air pump.
I decided on my setup as based on the desire to not have the generator running while I was away from the motorhome for two or three hours, and still having the ability to have a meal cooking in the slow cooker or be making ice in the ice maker.
The Go Power site has a handy calculator to help decide what is needed for what applications, and there's a real informative video on the Gone with the Wynns site.
Gone With the Wynns
Mobile Power Systems and Solutions for RV, Utility, Fleet and Marine Application