Please help me choose one version of Fedora for my computer

[Qiang]

Few days ago, I got one new computer.
Next, it is the specs of the machine:
*--------------------------------------------------*
CPU:       Intel Core(TM)2 Duo Processor
Mainboard: ASUS P5GZ-MX
Memory:    Kingston DDR2 SDRAM 1024MB
Harddisk:  Seagate SATA 250GB
*--------------------------------------------------*

I wonder which version of Fedora is suitable to my machine,
i386 version, or x86_64 version.

I am not clear about the cpu.
Is it 64-bit cpu or 32-bit cpu? 

Well,
please help me choose one version between i386 version and x86_64 version.