On January 26, the American National Institute of Standards and Technology released Special Publication (SP) 800-163, Vetting the Security of Mobile Applications (link opens the PDF version of the document).
While the publication’s intended audience is IT administrators, the content is valuable for privacy-concerned individuals as well. I recommend skimming through Section 2, “App Vetting Process”, and considering the application of the overall vetting and approval process to the apps you use most frequently (e.g. your email, SMS, or search apps) and the apps that you trust with the most information about yourself (e.g. your cloud storage, camera, and banking apps).
Taking a little care in handling your own information can make a big difference, and once you get used to considering how information travels through the apps you use as part of your pre-installation concerns it doesn’t even take much extra time.