I'll leave the discussion of the difference between Build Tools, Platform Tools, and Tools to others. From a practical standpoint, you only need to know the answer to your second question:
Answer: Use the most recent version.
For those using Android Studio with Gradle, the buildToolsVersion
has to be set in the build.gradle
(Module: app) file.
android {
compileSdkVersion 25
buildToolsVersion "25.0.2"
...
}
Open the Android SDK Manager.
The last item will show the most recent version.
Make sure it is installed and then write that number as the buildToolsVersion
in build.gradle
(Module: app).