It is possible to run a gui on such a system, I have a laptop with the same spec. Just about any distro will work it just depends which gui you want to use. The stock kde or gnome is out of the question, (with some playing around it would be possible). Something like xfce would work, but in my opinion it is still to big. There are more out there.
My personal preference for a gui is window maker. I run this on all of my linux machines (that need a gui), it is very basic gui compared to the likes of kde, gnome, xfce and others. But it is light weight and fast.
And again my personal preference for a distro is slackware. It does not hide the config behind pretty graphical programs, instead it makes you learn how linux really works.