Cattelya – This orchid is probably best known as the corsage flower, since that is where most people first see it. Of the different varieties of orchid, this is the standard that most growers refer to. Cattleya is a native of South America and loves heat and light. Grow them in rooms that feel almost stuffy and place them where they can get as much sunlight as possible without burning them.
Disa is a genus of beautiful plants with rather triangular flowers, often red. They require VERY different care than other types of orchids, so it's easy to kill them if you don't know what you're doing. In particular, they like it wet and should never dry out. The best-known Disa is Disa uniflora, which in South Africa is known as the Pride of Table Mountain.
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.