Almost any new computer with a dedicated GPU (video card) will run the Sims 3 Fine, My kids ran it flawless on a old Dell XPS-400 with a X1900GT. I upgraded them to a HD4850 and it runs better.
Even onboard Video will run the Sims 3. Remember that a new CPU at 1.8 Ghz is faster then a 2.4Ghz P4.
For the Sims 3 to run you can buy any computer that has Windows 7 or Any MAC today and it will run it fine.