both the dark spots and the light spots are due to cumulative sun exposure over years. what you do now may help prevent the spots from getting darker and will make it so you get fewer new ones over time but they are really markers of what happened 10-20 years ago. there are excellent sun protection products that are oil free or are designed for oily skin and i would recommend looking for those in particular if your skin is oily.
i use a high spf lotion on my face daily and have sensitive oily skin. why do i still get sun spots and white freckles?