If you want to grow plants on driftwood that is totally up and out of the water then you want to use epiphytes, such as orchids, bromeliads and epiphytic cacti.
If you want to grow plants on wood or riparium planters that are down in the water then you want to use emersed/marginal aquatics.
These two classes of plants are very different from each other. Epiphytes will drown--their roots will die--if you plant them in the water. Marginals will dry out too quickly if mounted as epiphytes.
For grocery store epiphyte possibilities consider smaller varieties of orchids like Phalaenopsis and maybe you can find bromeliads too. There are some good Dischidia and Peperomia that are showing up regularly at Home Depot.
There are a number of common and easy aquarium plants that will grow very well emersed as riparium/paludarium subjects. The most important consideration for these is their respective humidity requirements: some demand very humid air all the time (crypts, Anubis, Java fern), while others grow best in somewhat drier air, as in open-top tanks (Echinodorus, most stems).
Really good houseplants for ripariums/paludairums include Spathiphyllum and Pilea, and a few others.