Phalaenopsis: need low to medium light and temperatures between 70° and 80°F. The "moth orchid."
Paphiopedilums: need low to medium light (an east or west-facing window) and temperatures between 55° and 75°F. Exotic relatives of our familiar lady-slippers.
Cattleyas: need medium to high light (a south-facing window) and temperatures between 70° and 80°F. The classic corsage orchid.
Equitant oncidiums (Tolumnea): need same conditions as cattleyas. Very compact growers. The "butterfly" orchid.
There are two other points to consider when buying orchids. First, although orchids bloom for a long time (sometimes months), when they're not in bloom, they're foliage plants. Some paphiopedilums and phalaenopsis have beautifully patterned foliage that makes them beautiful even when not in bloom. Second, orchids can take years to reach blooming size. When you buy a plant, specify "blooming size" to make sure it will flower first year.