I am also on my first grow and I will just warn you of my first mistake I made. Make sure the tub that you built is completely light tight. I thought mine was, but found out that light could still leak through the plastic. If you can, hold your tub up to a light while looking from the inside, if any light is getting through, there's a good chance of fungus growth. Also I would recommend at least another air stone, the more bubbles the better. Last thing is that with bubblers you want to make sure your water temps stay around 70*F and not much higher. If water temps can't be kept this low, I have found that using Hygrozyme has allowed my water temps to safely be a little higher.
I didn't know the importance of all this starting out and ended up with root rot, and that was no fun.
To solve the light leak issue, I now paint the tubs first with a couple layers of black paint. Then a couple layers of white paint. The black is to block out light, the white is to reflect light and help keep temps down.
Hope some of this may have helped you.
Happy Growing.