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.
The main characteristic of this type of orchid is its very pleasant aroma, which means you will likely smell it even before you see it. The pure white flowers release their scent at night, are frequent bloomers, and can bloom all year long in many places. They are a small but showy type of orchid, and their leaves are long, reed-like in shape, and light green in color. They are also easy to grow and are low-maintenance flowers.
Phalaenopsis, the Moth Orchid, is one of the most commonly available and easiest to grow orchid genera. It is an especially good choice for beginners to orchid growing. They have large, showy flowers that come in a wide variety of colors. Most species have several flowers per stem, but some have more, and others have as few as one or two. There are a great many hybrid varieties on the market.
The Bulbophyllum orchid genus is the largest in the Orchidaceae family, with over 1800 species, making it the third largest genus of plants. (Taxonomists will probably eventually split it into several smaller genera, but with so many types of orchids it's a massive undertaking!) They differ widely in appearance, but all have a single leaf emerging from the top of the pseudobulb, flower stems coming from the bottom of the pseudobulb, and a hinged lip designed to tip insects against the column. Many are pollinated by flies, and stink like dung or rotting carcasses, which is a great conversation starter and gives you bragging rights for putting up with it! (They don't all stink, fortunately.) The rhizomes wander all over the place and often branch freely, so it's easy to grow an impressive specimen.
Phalaenopsis, the Moth Orchid, is one of the most commonly available and easiest to grow orchid genera. It is an especially good choice for beginners to orchid growing. They have large, showy flowers that come in a wide variety of colors. Most species have several flowers per stem, but some have more, and others have as few as one or two. There are a great many hybrid varieties on the market.

Phalaenopsis, the Moth Orchid, is one of the most commonly available and easiest to grow orchid genera. It is an especially good choice for beginners to orchid growing. They have large, showy flowers that come in a wide variety of colors. Most species have several flowers per stem, but some have more, and others have as few as one or two. There are a great many hybrid varieties on the market.
The seeds are generally almost microscopic and very numerous, in some species over a million per capsule. After ripening, they blow off like dust particles or spores. They lack endosperm and must enter symbiotic relationships with various mycorrhizal basidiomyceteous fungi that provide them the necessary nutrients to germinate, so all orchid species are mycoheterotrophic during germination and reliant upon fungi to complete their lifecycles. 

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.

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