Generally textures are the largest memory consumers, so using procedural textures will reduce the memory requirements dramatically. The size of the render will have some impact as will the number of lights.

Carrara will use a dual core processor (during any render) (and should be able to use a quad core) and can use a network during batch renders. It is a 32 bit program, so it can only use 2GB max (with dual core memory use may increase to 3 GB max).

Most people are currently (and in the near future) running a 32 bit version of Windows. Although many people have a 64 bit processor, few actually use the capabilities. Even Vista can only access 4GB in some 64 bit versions, so you will need a motherboard capable of using more than 4Gb (currently rare), a version of a 64 bit OS and correct drivers (difficult) and a 64 bit version of the executables (very rare at the moment) to actually use more than 4GB. Within a few years this is all possible but for now we will have to accept the current limitations.