I think the spectrum is important for best results - so the selection of light types might be best for a forum that deals with inside growing - or get some standard grow lights and then a simple program for the time with large enough relays or Triacs to switch the load
But the time inside the Arduino seems to creep a bit so a real time clock might keep you from needing to fine tune the time settings - or you could just go with a simple program of X time / minutes on and Y time / minutes off - would be also straight forward