Makeup can only cause damage to the skin and cause breakouts only if you are not taking care of your skin. It is SO important to wash your face every night. And also Make-up brushes hold a lot of bacteria so make sure to wash them every two weeks to a month. I promise you as long as you are taking good care of your skin and washing it at night then you should be fine. Also try to stay away from any foundation that has Mineral Oil. . Here are a few that I recommend, but they are just a few dollars over your budget. Hope that's okay.
Sephora Pro Artist
The majority of makeup is going to disturb the natural balance of your skin. No matter if it's named "natural" OR you can sleep in it or whatever the claim may be..think about it you are putting a layer of something on your skin that doesn't belong there. So your skin is going to absorb it. There's no evidence that makeup causes aging..but irritation from the skin can cause premature aging. I suggest to find a full coverage foundation with some good ingredients incorporated into the formula. Think antioxidants, chamomile, aloe vera, oatmeal, things like that to help soothe skin. I second the Tarte reccommendation.