Choosing Garlic Varieties
Remember you are planting in the fall so don't order garlic in the spring.
There are two main kinds of garlic. (Actually, there are three. The third kind, 'elephant garlic', Allium ampeloprasum, has absolutely enormous cloves, but has no garlic flavor worth mentioning.)
The first is 'Common garlic', which is the usual white skinned supermarket type plus the silverskin types generally used for braiding and available at farmers markets; and the second is 'Hard neck garlic', which is much less common.
Common garlic
There are two main 'types' of common garlic - the so-called 'artichoke' garlic we buy in the supermarket, and the 'silverskins', with either very white, or white blushed rose outer skins.
The bulbs of the common 'artichoke' types outer parchment is white, or off-white. There is usually a row of decent sized cloves around the outside, and irritatingly smaller, thinner cloves in the interior (although there are varieties with few, but quite large, cloves).
As we all know, removing the skin from these cloves is not easy. The bulb is wrapped in many layers of parchment, which continues up to form a soft parchment like neck ideal for using to braid all your bulbs together on a string to hang in the kitchen! This garlic keeps well. Silverskins have the strongest flavor, and have numerous small cloves. They are very white, and the neck is sturdy and well suited to plaiting.
Hardneck Garlic
These garlics have a stiff, sometimes thick, neck, usually with fewer, even sized cloves arranged around the central 'neck'. Cloves number from four to twelve or so, depending on the variety. They are generally less reliable in changeable weather conditions than soft necked garlics, with the exception of the rocombole type.
The most distinctive of the three main hardneck types is 'Rocambole' Garlic. This garlic is similar to common garlic, but has two important differences. First, unlike common garlic, it throws up a flowering stem, called a 'scape'. Second, the bulb has relatively little outer parchment. This last difference has a positive and a negative side.
On the negative side, the individual cloves are often exposed, can be knocked off the bulb by rough handling, and can wither a bit after long storage. In addition, the bulbs don't look anything like as attractive as bulbs of common garlic.
On the positive side, they are a dream to remove the skin from -it is trivially easy- there is only one ring of decent sized cloves arranged around the woody central flower stalk and no smalls or thins, and it keeps almost as well as common garlic if stored carefully.
The tall flowering scape , for reasons of its own, makes a twisting loop as it unfurls it's 'flower' head (which contains not flowers, but tiny little bulbils). Thus it's alternative name, 'serpent garlic'. Clipping the flower stalk off early on significantly improves bulb size.
It needs a cool winter and spring, and simply will not succeed in hot areas. 
Purple Stripe Garlic has very white, thick, bulb skins, streaked with bright purple. They are quite a variable group, with some strongly flavored, some mild, some mid season,some late maturing. They store fairly well.
Porcelain Garlic includes varieties with few (4-8), large fat cloves covered in a very thick, very white bulb skin. The taste is usually strong. They store moderately well if free of disease.
California Early and California Late need cold exposure of around 6 weeks below an average of about 4C/40F for proper bulbing and clove development. It is the classic, white skinned garlic 'artichoke garlic' of the supermarkets.
New York White (syn.Polish White) White parchment, slightly blushed with purple, said to be relatively disease tolerant, and better adapted to temperate than warm temperate areas.
Creole This silverskin garlic is quite a late maturing variety from Central America ( also grown in the Imperial Valley of California). It is adapted to heat and dry conditions, and doesn't do well in more humid and cooler areas. The cloves have a deep purple skin.
German extra hardy A hard neck garlic with a white outer parchment and red skin on the cloves. Noted for it's vigor, strong resistance to winter heaving in temperate areas, and good storage ability.
Roja A fairly common home garden rocambole type with attractive, brownish-red, medium-sized bulbs.
Continental garlic Is more of a generic term covering various white or purple striped hard neck types adapted to more Mediterranean growing conditions.
Elephant garlic, actually a type of leek, produces large, mild-tasting cloves, usually fewer per bulb than the true garlics.