A 1000 VA inverter is pretty small compared to the power needs of even a small home. Think of it this way, the average power drop is a 240V, 100A single phase, dual voltage (120, 240) setup that can run a full-time load of 18,000 Watts all day long. Your 1000 VA inverter (I'm assuming that it's not a pure sine wave model. and therefore can't power many motors, your air conditioner or refrigerator for example) is about enough for you to watch TV. The average battery that powers it will let it run for maybe an hour. Unless you're extremely talented at conserving energy AND have other sources like solar and wind, 1000 VA isn't going to get you into the 20th century.
My advice is to invest in a >3000VA genset that runs on the fuel that runs your camper, or the propane that runs other things. 3000VA will still leave you needing to conserve energy, but is a more realistic power source. If you have the capacity to carry a ton (literally!!!) of lead-acid batteries to feed a 3000VA inverter, that's a legitimate alternative. I'd still keep a ~100 lb. generator for security, but rely on a literal ton of batteries to run a ~3000VA pure sine inverter. I'm a trained electrical engineer, with $100,000 in '80s dollars invested in that knowledge. If you're not as highly trained as I am, your results will vary...to the negative.
If you're relying on a genset (motor running all the time), plan on spending $3000-5000 to install it. If you want to use battery power, plan on spending as much, with less run-time. Don't think for a minute that you can recharge a bank of batteries with a 12V, 200A (that's aftermarket, not stock!) alternator. That high output alternator is needed to keep your rig running as it drives, and can't do more than that.
If what I'm saying seems like Greek to you, seek the help of a RV professional. Do keep your 1000VA inverter, with a dedicated deep cycle battery to run it. I suggest the biggest Sears DieHard PM-1 deep cycle battery (~75#, ~$200 ea.) to feed your inverter. I own two Sunforce 1000VA pure sine inverters. One can power my 5000 BTU A/C unit for an hour, and the other can power the other things all night. If I tie both batteries together to a 2500VA modified square-wave inverter, I can do everything except turn motors. I can turn motors with it, but the efficiency sucks, and is a big waste.
Use your prime mover (automotive) motor and A/C for air conditioning during the day, and plan on having no A/C at night. Likewise, use your prime mover, a gasoline, Diesel or propane powered genset to keep your food cold. A relatively small lead-acid battery can run LED and/or fluorescent lighting all night. A 1000VA inverter with a single deep cycle battery will give you lights, a couple of fans and limited TV and gaming. The battery must be recharged every day. This can come from a high-output, dual battery charging system, which can be augmented by a solar array. Don't think that the solar array will provide enough power unless you're a real electrical engineer. It can be done, but don't expect Utopian results.