16 hours light will be plenty, 14 is reckoned to be minimum.
Coincidentally (or maybe not) we're sitting at around 14.5 hours daylight right now and dropping around 4 mins per day so i've been using artificial light in mine for the last month or so.
I take it you are too far from a mains supply or just specifically looking for a solar powered option?
It doesn't need to be high intensity, I can't remember the actual lux figure (and it might not help you much anyway) but the old method I was taught was that if its bright enough to read a newspaper its bright enough to make the hens lay
I have a 12v system in my laying shed (its 8' x 6' not a huge farm)
I have a small 12v solar panel on the roof which trickle charges an old (but good) 12v car battery.
Off this I run a 12v timer and two 3w 12v bulbs (in parallel in case one blows) and this gives more than enough light in an 8 x 6 shed.
My 16 hour day length runs from 5am to 9pm so I currently have my lights on from 5am till 7 am and 7pm till 9 pm.
As the natural day length shortens i'll alter the times to cover it, although it will always start at 5am and finish at 9pm.
I have mains power to the shed via an extension from the house which I can also use for lighting/charging if needs be but I try not to (i'm tight)
Cost wise it was roughly :
Solar panel £20
Timer £8 (eBay)
bulbs free (pinched them out an old car)
Battery (as above)
I have been thinking of "updating" my system to LED's to reduce the power consumption but its not really needed.