I have an Acer Aspire 7735G. It's a bit of a monstor of a laptop. Has dual core, 4B ram, 17" screen, full size keyboard, etc. Not quite as portable as a laptop should be but it runs the sims ok, although I can't run it on high graphics as it lags. With all laptops it is the graphics card that will hold you back. My graphics card uses on board memory, so with 4gb its not too bad. And I can easily switch between the sims and desktop and have programs running in the background at the same time.
There are two options you can take. Firstly I would seriously consider re-furbished laptops. You get a fair amount of money off with them and they're as good as new. Mine's refurbished because it had a small scratch on the case! Knocked off £200. Secondly, if you can get a laptop that will allows to to replace the graphics card at a later date. Laptop graphics cards are more expensive than desktop ones, but it'll be worth it for when you have that extra money and want to play the sims on full graphics.