What 3DS Max Version to use and Where to get the FBX Exporter?

As for what is the best that suites Unity, I'd say that it depends on what you are comfortable with. Personally, I would go for Blender if you are looking for a free solution because of the wealth of free training and 0 licensing issues since it is open source software. If you plan to monetize your assets and/or sell your game, the student license might not apply.

As for the FBX Exporter, I believe all [most] Autodesk tools come with the functionality built-in to the software. You should be able to find it under the Export menu in 3DS Max. Also, Blender has an FBX Exporter as well if I remember correctly, if you are wanting to use FBX.

Now you've spent a week with Unity, it's time to get acquainted with the documentation that comes with it. The docs are installed on your machine, and also online. The page here:

http://docs.unity3d.com/Documentation/Manual/HOWTO-ImportObjectMax.html

will tell you probably all you need to know, including a link to the Autodesk site where you can get the FBX exporter from. The screenshot on that page shows version 2013.3, so that's a good one to get.