Here is a very simple one way system that does not require any pumps. The nutrient system is simple to the extreme too.
One way systems have the advantage that they eliminate problems of toxins building up in the nutrients and also eliminates cross contamination problems. I built it outdoors so I don't need to provide any lighting either.
First: I built a 10 ft. X 10 ft square redwood sand box and filled it with about 85 cubic ft of washed building sand (It's washed before you buy it). I prefer building sand because it doesn't have any biological matter in it, and the medium and coarse grain sizes provide excellent aeration.
Second: I ran four 180 deg. micro-sprinklers from my magnetic pulse valve
SpritzWiz™ Intermittent Sprinkler Irrigation . I put a sprinkler at each side of the box. The magnetic pulse valve produces intermittent pulses of water to the sprinklers. It delivers water at whatever rate you set it at. No pumps are needed because the the water comes directly from your faucet, and is already under pressure.
Third: I sowed the seeds into the sand and then sprinkled some Osmocote® slow release fertilizer beads on top to cover the 100 sq. ft area. The container indicates the dispersal concentration of fertilizer beads that is needed. I repeated the fertilizer application a month later.
Fourth: I turned on the water faucet. I set the magnetic pulse valve to deliver water at a rate of 1 Gallon/Hour ( about 1 second pulses every 60 seconds). I left the water on full time for the first 6 days until all the seeds were germinated. I then cut the watering back to 10 hours per day and kept the same flow rate of 1 Gallon/Hour. I turned the water faucet on and off manually but later used a Dig® Model 9001DB "low flow" Water Timer to do it for me. I programmed it to go every day with 4 watering times of 2-1/2 hours each to cover the daylight hours. It was turned off at night. The sand never dried out and kept the plants healthy.
Final Note: The water consumption for the 100 sq. ft. plot was only 10 Gallons/Day and I only needed to sprinkle on more fertilizer two more times.