Actually, Unity desktop in Ubuntu will eat all your memory. To run anything will cost looooong swap times. If you can add the memory up to at least 2GB, then you can be fine. If you have low memory, you can help the performance by lower the swappines parameter (follow this question: How do I configure swappiness?).
Better you choose Xubuntu or Lubuntu with such configuration or increase amount of memory if you want to install Ubuntu+Unity. Option for Ubuntu could be to use Gnome classic or XFCE sessions.
CPU is OK, it is not a hit of last years, but will run your system and some set of basic applications relatively smoothly.
HDD - Ubuntu will take some 5-20G from your HDD, depend on set of app and the rest is for your Documents etc.