Asking me what types of orchids there are is like asking me what types of people there are. Well, there are tall and short people, smart people and not-so-smart people, introverts and extroverts, people with different skin colors, and people from different parts of the world. Likewise, you will find many different types of orchids—different colors, species and hybrids, miniature and standard-sized, all different genera from different parts of the world. So I will narrow the question a bit, and look at it in terms of the orchids you will likely to buy and grow.
Cymbidium carry tall stems with many flowers that have a more typical orchid shape. They are easily identified by their grassy leaves, and they readily form large clumps. Most common are the cool-flowering types, which need to experience a cooler winter (nights in the 40s for some time in the fall) in order to initiate flowering. Once the flowers open, they can last for up to two months or more, especially in a cool environment. These are very showy and rewarding plants, and a plant in a six-inch pot can carry three stems with 15 or more flowers each, depending on the type.