I would probably go even smaller than the suggestions above, maybe only 600 watts. The TV + DVD won't be over 200 watts, but I'll bet you end up with some other things as well, e.g. computer, cell phone charger, etc.
Place the inverter close to the batteries if possible, but it should be in a ventilated area (they get warm) and preferable not real close to the corrosive gases that a flooded cell battery may release. But if the batteries are a sealed type, e.g. AGM, then gases are not a concern.
You definitely need more battery to use an inverter. 200 watts @ 12v takes a steady 17 amps from the battery bank, so 4 hours of tv & dvd is 4 x 17 = 68 amp-hours. That's just about the entire capacity of a Group 24 size battery (around 85 amp-hours) and you really don't want to use more than 50% or so of the available AH if you want the battery to last more than a year.
Two Group 27 size deep cycle batteries would give you about 210 AH of battery power, or about 105-110 AH at the 50% level.