I'm using IBC based system and will end up 2 1000 liter tanks and 4 growbeds plus a few buckets and seedling trays. I'll initially use a standard mains sump pump because I've got a couple. the flow rate to flood and drain four grow beds isn't that much, I worked out that 2 standard 'fountain' solar pump would give you enough flow to keep fish healthy and 4 grow beds fed.
I'm planning on breeding trout, with a low stocking rate to give bigger fish.
I will use pellets but supplement from worm farm and maggots from waste. I've had half a dozen small perch in one IBC for about months without feeding them at all.
I intend using some fish for stocking a friends lake, and would re-stock with fry. You can also breed trout in captivity, though I don't know how yet.
When I had my pilot system it found it's own balance and I was very pleased with the results.
I tried a 'hybrid' version of Quackaponics but not a closed system, but it certainly made the beds more productive. I basically pumped the dirty duck pond water into a bin and then had irrigation lines that trickle fed soil beds. I initially had problems with blocked pipes, but added more water and that seemed to sort the problem. The soil beds with duck pond water did much better than the clean water ones. Foxes have caused us with a continuity problem though.
I'd not come across peeponics, but I'm already looking at building a system - Thanks very much