IMHO you are starting in the middle then working toward three ends.
1. Take the batteries to a genuine BATTERY SHOP. A real one. Not Wal Mart and have them charged and checked.
2. My satellite system gulped SEVEN AMPERES of power from the batteries. So it is nowhere in hell as economical powerwise as a DVD player.
3. You NEED a wall mounted amp hour meter to keep tabs on where your battery charge is or isn't. Guessing or using simple voltage just does not cut it.
4. Got a regular TV? Put your hand over top. It serves as a modest heater as well. An LCD television is the way to go. Folks here on this forum will guide you well.
5. Forget about switching inverters. Save your money. Like fitting new tires to a burning car. Use your money for something useful.
6. When you start your generator you want it to charge batteries QUICKLY not sit there, vibrate, roar, empty your wallet and play with itself. Again fellow forum members will help steer you right.
START WITH THE BATTERIES. Go to the yellow pages and find a battery shop. Interstate DISTRIBUTORS (not retailers) used to offer this service or recommend a shop whom they trust.
With ten seconds if I dwaddle, I can tell how much power I used overnight, how much charging I am going to need to bring up my batteries, and whether what I believe to be a charge taking place, really is. It is that amp hour meter I mentioned earlier. Lots of advice here if you ask for it.