What is the best way to turn my old Android tablet into a 100% VNC client?
Possible Solutions for Android 2.1 enabling VNC protocol are :


VNC Viewer
VNC Viewer for Android
Remote VNC Pro
Remote Ripple: Fast VNC Client
VNC Client Free
Remote VNC w/Ad
In-Hand VNC
Remote Ripple PRO (TightVNC)
vmwViewer
abtoVNC Viewer
VNC4Droid 1MA


Apps Enabling RDP protocol are :


Remote RDP
im Remote Desktop, RDP +


Note :- All the aforesaid apps are available on Google PlayStore. 1MA implies app available on 1mobile.com only. The answer has been overhauled on the basis of comments received.