Succulents, Cacti, African violets, miniature orchids, ivy, bamboo, miniature palms, spider plants, Peperomia plants, Syngoniums, some ferns and many more. Buy them at local nurseries, grocery stores, big box home improvement stores. Note every Omni-Pot comes with a 2" round plastic pot, allowing you to make your own plant from cuttings, seeds, or transplants.
Before I start let me qualify my answer. I am not a plant expert but have been around them all my life and have a bit of green thumb so will make some suggestions that have worked for me.
First thing to know is the Omni-Pot holds 2" Round or Square plastic pots, so that opens up some options and prevents the need for transplanting. Most of the small plants we have found seem to be split about 50 / 50 between the two shapes.
The second thing to know is that each Omni-Pot ships with a 2" round plastic pot, so you don't have to buy a plant. This allows people to make their own mini-succulent gardens (as seen in the video), plant cuttings, grow from seed, or transplant something. Omni-Pot is about options options after all.
That being said, we did purchase most of the plants that are currently living on our walls. We bought them primarily from local nurseries and some from grocery chains like Trader Joe's. Big box home improvement stores also sometimes have them. Found some cool 2" tiny Christmas trees last year.
As for plant suggestions, succulents work great in Omni-Pots. They don't need water as often and are generally "tough" plants. Same goes for Cacti. Cactus don't need much water and grow slow.
However there are also lots of house plants that do well in a 2" pots. Here are some ideas: Ivy of all kinds, African Violets, Miniature Orchids (my personal favorite, get them at Trader Joe's), Bamboo, Peperomia plant, Spider Plants, Rubber Plants, Wandering Jew. Syngonium, Miniature Palms and some Ferns. Last but not least, Omni-Pots are great for small herb gardens.