Dual screens. Make sure graphics hard has lots of dedicated memory , ( no sharing with main memory ) if you want to use 3d.
64 bit os is not required as altium is a 32 bit apps. The problem is borland isnt ready with 64 bit compiler .... Altium is written in Delphi...
I believe with altium 12 this will change.
Quad core cpu is fine if you have two windows open plus some other programs. Each altium window will use one core. So you will not 'feel' a slowdown when running dual monitors.
Three or more screens is recommended if you start doing the simulation and fpga stuff. You simply want to have everything open becasue of the powefull cross probing.
But, do yourself a favor : get a 3D spaceexplorer... That little 90$ peripheral makes altium thoroughly wonderful. Zoom, pan , scroll, rotate is so smooth with that thing you will wonder how come not many more programs support it.
It also works in google earth , acrobat reader and many other cad programs.