TODO: Where should this live? It feels a little out of place here.
You will spend most of your time in the IDE, so it makes a lot of sense to get comfortable with this tool!
Google is deprecating the usage of Eclipse + ant over time. They have forked IntelliJ to create Android Studio and have switched their build tools to gradle.
Since this is still an emerging IDE, I prefer to use IntelliJ and maven for the best intersection of tools at the moment. Luckily it should be fairly trivial to switch to gradle since it uses a lot of the same mechanisms of maven (but it is not trivial to switch from ant to gradle/maven).
This useful tool can be used to take screenshots, manage memory usage, and track down memory leaks.
This is used to shell into your Android applications, copy files from the device, push files to the device, and install applications from the command line.
This is the phone's log. You use this for debugging and monitoring purposes.