I have considered African chiclids also. The problem is their ph requirements are too high. You want to stay 5.5-7.4 with 7 being the best compromise, otherwise you get nutrient lock out on the hydroponics piece. Most leafy greens and kitchen herbs would probably still be ok, but you wouldn't produce very nice fruits.
I know for a fact that oscars work. Seen it done, and they arw food fish elsewhere in the world.
You want a hardy fish tolerant of dissolved minerals, since the grow bed and infeequent water changes will accumulate lots of trace.
Temp needs to be 68-82 with optimal around 72-75, though mine ran at 80-82 with only brocolli and bush beans as the casualties. Some say, the more mature your system is, the more lee way you have with parameters
Take these parameters in mind and rainbows are a good option, along with rasboras and many cories. I kept turqoise rainbows, panda cories, and harlequin rasboras in mine with good results.