If you want to do more than 1 week veg, you will probably only want 2 plants in there, or they will have root problems with too little space, no matter what you do. You can put the screen thing in there, or just put a screen peace over the return feed hole. Also, I would probably throw an air stone in there because those roots sitting in the water without good Oxigen can get root rott. Last thing, if you just use hydro ton, or clay pellots as the medium you can keep your drippers on almost 24 7, and that equals more oxigen to the roots and better growth.
How many plants did you want to put in there? Good job, keep it up.
Adieu