Most plants can be grown aquaponically. Limitations arise due to the need for stability. Float beds/rafts will not be stable enough to support a top heavy crop like peppers, cucumbers or tomatoes.
The media bed is a good place to grow top heavy fruiting plants because the media will be able to anchor the plants.
In general, leafy greens and herbs have a very good track record. Some plants will not due well but this is usually a cultivar specific attribute, some types/cultivars just don’t positively respond to hydroponics/aquaponics.