Keep your garlic away from the refrigerator, or any cold storage. Garlic germinates after exposure to cold, which is why it's planted in autumn. This means that putting your garlic in the refrigerator is a bad idea as it will cause it to sprout, which creates undesirable changes in flavor and texture.
The garlic you buy at the store has been cured (dried) and will last for months at room temperature, and that's the best place for it to be. Garlic pots are better than sealed containers because they have holes that allow airflow, keeping the garlic from getting soggy while protecting it from sunlight or other strong light. I grow garlic and make my own garlic strings and braids, which I hang in my kitchen, I always make sure they are hung somewhere out of direct sunlight, but if I wasn't putting them out for show I would keep them in a cool, dark cupboard.
Here's a picture of my garlic pot, although there are many designs out there.