That's probably sufficient. Don't let the soil get dry between waterings, seeds need more constant moisture than established plants do. Most veggie seeds don't need light until they poke their heads up above the soil surface, since the soil is blocking out light anyway.
Peppers, in particular, need warmth to germinate, and I think more warmth makes them germinate faster. The soil temperature is supposed to be at least 65 degrees Fahrenheit, and as high as 95. They also usually take at least 10 days to germinate (and mine took over two weeks), so don't worry if they don't come up quickly. If you have a warm place to put them (I put mine above our woodstove on a high shelf) they will probably do better until they germinate. Then, once a lot of them have sprouted, put them where they'll get some light. The covering with plastic thing can work for that, but I always end up getting algae on the surface if I cover, so I don't. If you think they're too cold and don't have a warm place to put them, I used a hot water bottle underneath the flats in a previous year, and it seemed to work. I learn more every year, and you will too - the great thing is that the plants really want to live and are pretty good at it if we manage to meet their basic needs. Have fun!