First of all, you'll want to know if it works. Hell yes! HERE is a Youtube video I made just recently. If you note the difference in the cos (romaine) lettuce plants in the early part of the movie you'll see the difference in size.
Here's the interesting thing:
The small size of the plants, that was after around six weeks of running the system with seaweed extract and fish emulsion in the water. You can't use harsh fertilisers because they would pollute the water for the fish. And I wanted the system to have the nitrogen bacteria before I put fish in, so I let it run for long enough to be pretty sure that the fish emulsion was rotting to ammonia, and the ammonia was being converted by bacteria.
The larger size of the plants, that's only two weeks' growth after the first few fish were introduced to the tanks...
I'm pretty sure that the fish excrement is far better for the ammonia / nitrite / nitrate cycle than anything else, and that I'd luckily built up a decent colony of bacteria that must have been just under some critical mass. But the growth has exceeded my wildest expectations.
So the history of the system has been: Two weeks of running the system with water only, to iron out plumbing kinks and peculiarities. Two more weeks with only half the grow bed full of gravel, and plants in that half. Four weeks with the grow bed totally filled and a few more plants. And then two weeks with fish in the tanks and a HUGE growth spurt of the plants.
I can now honestly say that even a tiny system such as mine is, can produce a significant amount of plant growth, and a larger system would probably provide a significant proportion of one's vegetable requirements.
By the way, if you're in Australia, and more specifically in Victoria, I can now build you such a small system (250 litres - 600 litres) for around $400-$600 dry, depending on how large a system you want and how expensive the pumps etc that you want. ("Dry" means without gravel.) Shipping isn't really an option for something as bulky as this, so it has to be close by. Next project will be wicking beds, and I estimate around $250 for a pallet sized wicking bed.