Warlock, AP is addicting, I'll warn you and others skimming thru. I'm new to this site, but I've been growing with aquaponics for a while. Some things grow better than others, but you need to know that aquaponic growbeds need about six months to season before 'flowering' plants do well. I'd start with lettuce, and move to tomatoes and peppers, then herbs. Nitrifying bacteria need to establish a population and they will go through spikes and poor water quality before finding balance. It is best to start with a seasoned fish tank and add tank, growbed, and fish volume gradually.
If you don't already have a seasoned fish tank, then start with adding some household ammonia to an otherwise complete system, including the plants but minus the fish. Once both the ammonia and nitrites have spiked and receded, then add fish. I shoot for 1 lb of fish to 5 gallons of water, to 10 gallons of growbed media (hydroton or gravel). So suppose you wish to use a standard 55 gallon aquarium. That will eventually support 11 lbs of fish and 110 gallons of gravel, or 22 five gallon pails. I grow catfish and tilapia, and eat them in the 1 pound range, so about 11 fish if they are all 1 pounders, or about 50 fish staggered in age to keep a perpetual harvest going. You can feed your fish commercial pellets. You will also have to add some liquid kelp for trace elements, possibly some Epsom salts, and definitely some chelated iron. Fish don't need iron, so fish food is generally not formulated to contain it.
Veging plants pull mostly nitrogen, and flowering plants everything else. Nitrates will accumulate harmlessly in the water while flowering and an abundance will be ready for the next crop, and vise versa. Or even better, use the same water to feed veg and flower in different rooms. Some folks use solid filters to prevent growbeds from getting clogged. I don't. I pump all the solids from the bottom of the fish tank to gravel growbeds and add a handful of composting worms to each one. Worms will eat the fish solids, uneaten fish food, and decaying plant matter (like leftover roots from the last crop). They re-consume their own wastes over and over again, each time gaining nutrient that was missed before, and the solids becoming smaller each time as well, until eventually the solids are mineralized into the water, making them available for plant uptake, thereby removing them from the system.
Sorry, long post. Anyway, happy to answer specifics if I can. Hope to start an aquaponic grow journal in a few weeks.