Hi,
I know how you feel! Im 20 now so my skin has cleared up, but I had problems with pimples/blackheads from age 14-17. Using products with salicylic acid can help, however they can be drying so moisturise afterward. Different things work for different people, and often in your teenage years its hormonal, so while you can help to clear some if it you will still get some hormonal breakouts.
Often using oil-free ingredients is a good idea, however you dont want to over-dry your skin. Sometimes oils actually help to balance oily skin! Jojoba oil, grapeseed oil, apricot kernel oil, safflower oil and tamanu oil are all supposed to be good for oily/combination skin. Check out some reviews online and read up about them if you are interested 🙂 I personally found tamanu the best for healing pimples and balancing the skin. If you do choose to use an oil, buy a pure one and only massage a few small drops onto a clean damp face, so that it absorbs better.
I find that products with mineral oil can clog my skin. I now use moisturisers from a brand called Moogoo. They have a moisturiser for acne called the Acne Cleansing Cream, which is pretty gentle and works for some people.