Shade, in full daylight, is about 10,000 to 25,000 lux (1 lx = 1 lm/m2, or 1 lux equals 1 lumen divided by 1 square meter.)
So assuming the lamp will be placed ~18" over the flat, and the luminous efficacy of a typical fluorescence is 50–70 lumens per watt, you will want something in the 250-350 watt range (NOT a 250 watt replacement... which has far less wattage than 250).
Also, designated 'grow lights', although generally far overpriced IME, have a more natural light range for growing plants. The next best are 'daylight' fluorescent bulbs. Also, there are many powerful and good LED grow lights on the market now, and although they are rather pricey for a small operation, they could potentially outlive you, and are energy efficient, and not as hot.
I know seems kind of bright indoors, but it's actually not nearly as intense as direct sunlight. Here's another thread that may be relevant to you:
About turning the lights off at night, that is beneficial, as there are processes that a plant naturally does at night more than in the day, and about all plants are day length sensitive to a degree. I'd say if you can, it'd be a great way to make it more natural for the seedlings.