Your tv depending on age will take about 2 or 300 watts, dvd about 10, lamp if low enery about 10, so a 600w genny would probably do the trick, and might be more economical.
Look at the rating plates on your devices and add them up, they should all say how many watts they need.
You could if you get lots of power cuts just get a tv/dvd player with a built in battery, I have one for the boats, it lasts 4 hours of a charge, and then just have a battery powered fluorescent lantern, might work out cheaper.
Gen sets being engine powered obviously put out noxious gases, namely carbon monoxide, however I dont think you've any intention of running one in the house!
Your house insurance might frown on a genny being inside the house, even for storage, due to the quantity of petrol.