how big is your budget?

What i would recommend is an ITX build, the parts are cheaper and they look awesome

I'd go with an AMD APU build. No reason to have dedicated graphics for a machine that's only going to run Sims 3.

http://pcpartpicker.com/user/perkymango/saved/#view=fxnV3C

My Build. May not be very budget friendly. But I can tell you this. It can handle Sims 3.

If you mum is in intel fan, like mine, go with a 4th gen i3, and a asus ftx 750ti for the graphics card. grab 8 gigs of ddr3 and a decent motherboard. That should be great