You won't need Vista Ultimate for a C2D. Even Windows XP and maybe Windows 2000 will support dual core processors, and all versions of Vista do. If you already have a copy of XP, it will work on your new Core 2 Duo, but if you're getting a 64 bit processor (which I think the C2D is, not big on Intel chips), you might want to at least get a 64-bit edition of Windows XP or Windows Vista. It's not necessary (64 bit chips can run 32 bit OS'es just fine) but if you want to get the most out of your 64-bit CPU and be able to run 64-bit applications, then it's recommended.
Personally, I still recommend XP, as it's more reliable and older applications work better on it. I would only go to Vista if I were going to get a DX10 compatible graphics card and play BioShock or Crysis or whatever on it.