The thing I know about aquaponics is that the more emphasis you put on the plant growth, the more Nitrate your fish will need to be tolerant to.
So If you're growing lettuce at "hobby" growth rates, you can get by with less Nitrates which will allow you more flexibility with your species choices, but If you are trying to grow something that is light an nutrient intensive (anything that fruits...like tomatoes, or...uh...a medical grow) then you will need a lot higher nutrient content in the water which will require a hardier fish to tolerate it.
Most Aquaponics people are using Tilapia...the food type... They are very hardy and very tolerant to high nitrate and other nutrients.
I breed and sell Tilapia. I would be doing aquaponics too, but I can't do it in my basement. Can't justify the artificial lighing expense, but It isn't too far away. Tilapia need long days to breed...but I need to put up a building before I can make it efficient on the scale that I would need to operate on. Since this is a business for me and not a hobby, It has to be profitable, not just cool.
I do a less direct version of aquaponics. I pipe all my fish water out onto my lawn and garden.
Mike