(This works for Acrobat X Pro. I don't know if Reader has the Accessibility options?)
The problem is in the Accessibility Setup. I was annoyed by this behavior also. I recently had to re-install the program and it defaulted to the select tool ever since then. I remembered that when first running the program after installation it launches the Accessibility Setup Wizard. If you take the defaults you will get the Select Tool by default.
Look under Preferences – Accessibility and uncheck “Always display the keyboard selection cursor”. Then select the Hand Tool. Then close the program. I have opened and closed Acrobat multiple times with multiple documents and the Hand Tool now remains the default.