Anyone with an oily skin should go for a hydrating, lightweight, and non comedogenic moisturiser that keeps their face feeling fresh and hydrated. The formula of the moisturiser should not be very creamy and it will be great if it is gel based, so that it locks in your skin’s moisture and keeps it from itching. Moisturisers with no or almost no fragrance are best as they are the most gentle on an oily skin , which is prone to acne and acne scarring. Also look for moisturisers with as many natural products as possible such as green tea extract, lemon, aloe vera, watermelon, or ingredients such as collagen in them. In a nutshell you should look for a preferably fragrance free, gel based, non- creamy moisturiser which has a higher concentration of natural ingredients. Again, everyone's skin can react differently to various products so it's always better to try a new moisturiser for a while. Most of the times, finding a correct moisturiser or other skincare product for sensitive skin can take a lot of trial and elimination. Hope this helps!