Both of my tanks are a sort of riparium, with some plants growing out of the water but no fancy planters or trellis raft thingies. I just clip little plants to the side with Christmas light clips so the roots can grow down into open water. The white clips are a bit unattractive for a while but the plant soon grows to hide them.
I have had success growing Epipremnum aureum (golden pothos), Draceana sanderiana (lucky bamboo), Hemigraphis exotica (purple waffle plant), Ficus pumila (creeping fig), Chlorophytum comosum var. variegatum (variegated spider plant), Ipomoea batatas (sweet potato) and Philodendron scandens (heartleaf philodendron). I hear peace lily, pilea, fittonia, and purple passion vine do well as well.