What ingredients in makeup and cosmetics should be avoided?

Nothing...: ...Unless you are allergic to a specific ingredient. If some makeups trigger a reaction on your skin, you can often determine which ingredient is the culprit by consulting a dermatologist who does patch testing (not all do) and asking to be tested with the "cosmetics tray". Cosmetic companies are often secretive about their formulas, so it is hard to pinpoint specific causes in some cases.

Sensitivity: I would advise seeking hypoallergenic cosmetics and changing them every several months to minimize bacterial contamination. Mineral based products genrally are less likely to promote bacterial growth.