Each Area51 light can cover a 2 x 3 area although a little smaller at 2 x 2 may be a little better. You would want at least two of these fixtures for a 4 x 4 space. These are excellent lights and should provide good service for a long time. Hans - bonsaihero.com - also makes a good panel...and there are others like rhino grow and apache. Hans provides fair recommendations for coverage as well...most manufacturers streeeeeetch the truth at best. I wouldn't purchase Blackstar - they have a reputation for needing repairs within about a year or so. You can easily supplement LED lighting - say sidelighting or in the corners, etc with fluorescent, if you desire/need due to the shape of your tent.
I built my own room and would recommend that you get something that is sturdy; it seems there's always something else that needs to be hung and everything is heavy. You don't want to ruin expensive equipment or a crop after you've put 3 - 5 months into the effort. I have heard that Gorilla tents are good but I'm definitely no expert on tents...just know that rooms take use/abuse so I'd look for sturdy and not try to cheap it unless you just have to.
A good exhaust fan is a must. If you can afford a variable speed one, you'll make it easier to control your environment. Good air circulation within the tent is also important so a nice oscillating fan for the space and a thermometer/hygrometer so you know the space temp and humidity.
You've said nothing about your grow style - maybe you haven't decided? Anyway, if you are interested in soil and possibly organic soil growing, I would go into the organic section here and start reading. I do soil only grows - little to no bottled nutrients - and have started recycled organic living soil (ROLS). There's also a good book that provides a lot of info laid out in an easy to read format - True Living Organics by The Rev. It's only $15 and easy to get from amazon. I don't slavishly follow any method but pick and choose and learn from many sources.
A good water source is something that you need to consider. Chlorine and chloramine are your enemies and hard water can make life difficult as well. Keep reading.