Memory usage will mainly depend on the desktop environment you are choosing, not so much on the distro. But some distros are available with lightweight flavors so you don't have to customize your self after the main installation.
To help you choose the right distro it would be helpful to know what you intend to do with the laptop.
Just internet / email / office apps or anything beyond that?
And what interface are you looking for? Would you prefer a windows-like point and click interface, or are you looking for a distro that encourages you to look under the hood and learn the inner workings of linux? (i.e. makes you use the command line)
You may want to try out some different distros as live systems, distrowatch.com
is a good resource to get an overview, but maybe start off with looking at
-Lubuntu (Ubuntu with LXDE Desktop)
-Mint XFCE (I think Mint is slightly easier to use that Ubuntu)
-Crunchbang (based on Debian, probably the most minimalistic but also the most lightweight, their artwork is a matter of taste, but I like it quite a bit)