Every skin type, including oily skin, needs to wear a moistuizer.  90% of all skin is dehydrated.   Oil is not water.  You can be extreemly oily and extreemly dehydrated at the same time.   Unless you are extremely dry, you will want to get an oil free moisturizer.  Most moisturizers that contain oil are occlusive and will sit on the skin (keeping your own moisture from escaping) rather than penetrate.  Everyone should use an eyecream.  The skin around your eyes is more delicate than the skin on your cheeks.  Your daily face moisturizer is not formulated for that delicate area and may actually cause puffiness around the eyes.  Some anti-aging eyecreams contain more concentration of the wrinkle fighting peptides than their complementary face creams. (You can use it on other areas that need more concentration to get the most benefit)