The fastest way to write a hello world application for Android using an IDE is to use Eclipse with the ADT and let those free products do the mundane tasks for you. Yeah, seems like cheating, but you probably want to use an IDE anyways and this gets you going in that direction. You can jump right into modifying the generated "hello world" program to learn by experimentation.
Here is how I recently wrote my first Android application using a Windows Vista machine. Everything downloaded was free.
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