Mainly garlic is classified in 2 types, hardneck which send up a main stalk that flowers (referred to as a scape that is great for cooking) and softneck that produce more bulb underneath. Hardneck varieties usually have a wider variety of colors and flavors and softnecks produce more and are typically easier to grow. Softnecks typically store for a longer period of time if processed correctly.
Rocambole, hardneck garlic varieties that are known for their great flavor and are used in a wide variety of gourmet applications.
Artichoke, softneck garlic varieties that are the ones you find in the store. Very easy to grow.
Music Pink Rocambole is a variety that we grow which is great for roasting and has a true garlic flavor. I would highly recommend this one.
Chilean Silver is a great Silverskin variety (longer keepers that enhance flavor over time) that keeps very well. It has a great flavor and produces a nice big harvest.
I would recommend going to a local gourmet shop (if possible) and taste some varieties to see which one you enjoy more. If that's not possible I'm sure there are some great varieties you could find online. Try a garlic supplier that processes garlic and look at their different varieties and flavor descriptions. Then see what works for you as far as growing conditions.
Good luck