While almost any terrestrial plant will grow well hydroponically, not all are suitable for a hydroponic growing aquarium or for an AeroGarden. There are a few container plants that will do really well in a 10-gallon aquarium by a window or underneath a grow light.
Some good plants to grow hydroponically in a hydroponic growing aquarium include:
Green leaf lettuce
Red leaf lettuce
Cherry tomatoes (this will grow large, so keep it pruned!)
And much more!