I know I wrote a lot. If you read nothing else, the best investment you can make today towards this goal is to upgrade your battery bank. You will need to do it for a solar setup anyway and if you choose not to go the solar route, more and bigger batteries will mean fewer runs of the genny.
When Fair Chase says its simple math, he is somewhat correct. Add up your power usage. A good place to start with this is called the
Kill-A-Watt
Measure your usage over 1 day, 3 days and 1 week or two if thats what you're going for. Once you've done your energy audit and you know what you need for power then you plan the power storage. A typical RV using a 12v fridge, lights, radio etc will use 25-40amps a day. Add in a furnace and you can double that amount, especially depending on the size of the camper.
Batteries: A typical 12v group 24 battery provided by the dealer is good for 75 amp hours, but to make the battery last you shouldn't discharge lower than 50%, so now you're only got 37amps of storage or about one days worth of power. Add a second battery and you double the days. A grp 27 12v battery or a grp 31 battery will give more power and more hours if you've got the room on the tongue. 2 - 6v batteries wired in series will give more power in the same footprint as two 12v will. Two 12v grp 27 batteries will get you 170 amps while two 6v in the same size will give you over 210 amps. Thats almost an extra day of power in the same footprint.
The fuzzy math described by nhn2a is that no part of electricity is 100% efficient, so everything has to be designed with the least amount of loss and oversized to account for short days and occasional bad weather. Additionally solar is designed based on power use AND battery bank size. they should be matched so as not to waste time, money or power. There are numerous websites and calculators out there.
I highly recommend HandyBob's blog. Just guessing on your setup, two Trojan T105 batteries coupled with 200-400 watts of solar and a PMW controller will suit you well.
Also, not sure what kind of electronics you're charging, but if they come with a car charger, they already charge off of 12v so using an inverter to charge them would be an enormous waste of power. Add some 12v sockets in your camper that are tied into the 12v system.
As far as running a TV, I can run our 32" flat screen and the blueray player on a 400 watt inverter without issue. Not much else requires AC power in our rig. Things like toasters, coffee makers etc are huge power hogs and require considerations when using.
TONS and I mean TONS of info on this topic out there. Just be careful of too many suggestions. Many people are willing to spend your money for you.