Hi Alexander,
Welcome to the wonderful world of Android!
I would suggest getting the updated software for Eclipse, the Android SDK, and also the ADT plug-in. These are required tools. The following link provides you everything you need to know:
http://developer.android.com/sdk/installing.html#InstallingADT
As for being restricted to a specific platform, you can use whichever platform you like as long as you download the required components.
Enjoy!
Jay