I would give Ubuntu a try, you can test drive it with the live CD before committing to it (ie installing it). The advantage of Ubuntu is that it's very good at detecting the host hardware and configuring itself and you would get a complete system. FWIW, I have Ubuntu running on an older netbook inside a Virtual Machine and it's workable so it's not that resource hungry. If you look around you'll find some smaller distributions specifically aimed at Laptops (though not so much in the recent past since laptops have become much more capable now).
Your biggest limitation on your system is the amount of RAM you currently have, if you can increase it, everything will work better all around. It may mean you have to replace one (or possibly both) of the chips already in the system depending on how the system is set up. Most systems only have max 2 memory slots, and others require identical memory modules in both of their slots.
Here are some links for more research:
How to choose the best Linux distro for laptops might have some useful information. And here's a discussion on LinuxQuestions.org about Best Linux Distribution for Laptop? (though this is from 2009)
Finally, from January of 2012 What’s the Best Linux Distro for Older PCs and Laptops? has some opinions to share.