What color lens should I buy for my polarized sunglasses? (ie gray or amber)

Choosing the color of the lens is about more than just aesthetics.   Knowing how each color will affect your vision is important for optimizing its utility for your specific purpose.  For example, I personally like to use amber lenses because it enhances contrast and detail when I am fishing.  There is naturally something called "blue haze" that is caused by blue light, and this creates a sort of blurriness that decreases the sharpness of your vision.  Because we are so accustomed to this blue haze, wearing amber lenses which filter out blue light can make your vision surprisingly sharp.  Amber lenses are also good for sunglasses that you use driving, since it will increase your ability to read signs and see details on the road.  The only downside to amber lenses is that your vision when looking through them will not have perfect color accuracy.   Since the blue light is removed, things you see won't have "true color".  If this is important to you, gray lenses may be the way to go.  Gray lenses do not distort the color, but do not remove blue haze like amber lenses do.  This could be important to some people since prolonged exposure to blue light can be irritating and even harmful to your eye and has been linked to development of cataracts over time. 

Often time a brand of lens may claim that the lense blocks 100% of all blue light.  This claim will be made even for non amber lenses such as grey lenses.  This is inaccurate because if you can see blue at all, its obviously not blocking out all of the blue light.  It is possible, however, to block out all the harmful blue light.  Oakley, for example, has an advanced filter as part of their lense that removes harmful blue light, regardlesss of the lens color, which is one of the many reasons I like their lenses.   This should not be confused with the practical advantages of removing blue light by using a specific color of lense (for example, an amber lense filters out blue light).  The special filter that is not color based, such as the one on Oakley lenses, removes the harmful blue light, but not neccessarily much of the visible blue light.  If the reason you want to filter out blue light is related to wanting to increase sharpness, resolution, and detail, while minimizing blue haze,  then you would still want to use a blue blocking colored lens such as an amber lens, which will help filter out both harmful and safe blue light (since you want to minimize all visible blue light).  For example, amber lenses are very good for hunting and fishing, since movement and detail are a lot easier to see.  Removing the harmful blue light by using Oakley lenses (which have the plutonite blue blocking technology) will give you the health benefits to your eye such as preventing cataracts, but will not give you the practical benefits (and drawbacks)that a blue filtering colored lens will give you.   This, however, may be a good thing as you may want to keep good color accuracy and want to filter out the minimal amount of  visible blue light.  In this case, grey lenses with harmful blue light blocking techology (such as Oakley's plutonite) is the practical answer for you.