Your computer can handle it, but it would be quite slow. The main weakness of your computer is your RAM, which I would suggest you to upgrade it at least to 2 Gb; if you can get it to 3Gb or 4Gb, it would be better, and you could easily handle Kubuntu or Ubuntu. Over 4Gb, it is almost Useless.
So, if you want to keep your computer as it is, and have an experience of a fast and reactive Operating system (I mean faster than Windows, which is always too slow for me, but I am really not patient), I would suggest you to go for Xubuntu (XFCE) or Lubuntu (LXDE). They are basically the same as Ubuntu, but with lighter desktop environment. LXDE is lighter than XFCE, but less customizable.
Here are the links for Xubuntu and Lubuntu
http://xubuntu.org/
http://lubuntu.net/