If you happen to have some dark spots and are desperate to see improvement, then you could start with your cleanser before stocking up on the skin lightening products. Look for a creamy one with niacin as an ingredient to help spur better skin along.
Just for the record, niacin is a proven aid when it comes to helping your skin with cell turnover. Other beneficial lightening ingredients to keep an eye out for are kojic acid, vitamin C, and licorice root, which also can come to your rescue.
To get the most benefits, try applying that cleanser directly to your dry skin and gently massage to clean away makeup and grime before rinsing.