I'm pretty much doing the same thing myself. I started off a lot more complicated then this though so I am glad to see someone keeping it simple. Some things I have learned:
That size light should probably be at least 12 to 18" away from tops of plants. The system you build will likely depend on how long you should water the plants. Don't be afraid to go 24h spraying time if your plants find that to be more suitable. I think a lot of the watering times people recommend really only work in their particular system. I have tried everything from 1 on 1 off to 30 on and 30 off. In the end I think my system requires 24/7 spray times as the plants seem most happy there. Also, the nutrients should be lower then what the bottle recommends by at least half if not more. Think about using water for the first week or more before adding any nutrients.

1. Do I need nutrients at first or just water until veg?
Water for the first week depending the size of your plants. Until they have at least a few sets of leaves they wont need any nutrients.

2. What the heck is VEG.. How much nutrients will I need to buy? I know I need to check PPM and PH so I will buy testers and up/down.

Veg is vegitative stage. Most people give their plants 18 hours light and 6 hours rest during this stage and they use a different set of nutrients during this process. They allow their plants to grow and get big during this time and not focus on growing flowers which is what you are really after. This process usually lasts about 5 weeks in the kind of setup your building. Some people skip this step entirely with the understanding that their plants wont be big or produce as much flowers then if they had waited till their plant was big. I would suggest allowing your plants to get at least 12" high during this stage but whatever target height you are wanting for a final plant size, about half is grown in the veg state. So if you want a 4 foot high plant then you will want to veg the plants until they are 2 feet high. Go to your local hydro store or poke around here for a recommended brand for aeroponics nutrients. I think Dutch Masters is a favorite brand on these forums. It will likely be a 4 part ( an A and a B for both vegetative and flowering cycles of growth) and it should definitely be 100% water soluble not a powder or your misters will clog more. For a ppm level try no more then 100 for the first week or two and then as the plants get bigger add more ppm's to about 400 or 500 at most for your kind of setup. Change water weekly.