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In addition to Christopher’s suggestions, I would add a couple of things:
1. Only install apps from Google Play or Amazon’s Store. A significant source of problem apps comes from people installing pirated apps to avoid ads. Either put up with the ads or pay for the version without them. Plus, developers need to make a living.
2. Restrict downloads from unknown sources. This will help prevent drive-by downloads.
3. No pron apps! I’m not being a prude, these types of apps are more likely to abuse your permissions and do things to cost you money.
All apps will inform you of the permissions you need to accept in order to download the app. If some of them seem unreasonable to you, I just wouldn't download it.
If you really want an app, however, you can use a tool such as SnoopWall that allows you to control which permissions to allow for the app after you download it. This article explains how SnoopWall works.