How can I select safe Android apps?

By safe I wish to restrict myself currently to NO .INTERNET in network permissions.

So is it possible to search for apps based on permissions? Otherwise how can I search for safe applications with so many of them having Full Network Access, without mentioning why they require it in the first place?

I can understand about network sockets for communication, network state etc., but why Internet access, when the apps dont even mention that they are ad-supported?

Thanks