I really like Sims 3. It took me a few days to get used to the changes in controls, but now that I have, I think it's way better than Sims 2.
It runs fine on my computer- apparently if it looks a lot like Sims 1, it's because your graphics card can't cope with having the graphics settings turned all the way up. Upgrading the drivers may help, but if you're also having slowness issues, your computer itself might not be quite powerful enough.