Ubuntu's default desktop interface will slow you down some. From Ubuntu you can install other desktops like Cinnamon which is used by Mint, LXDE which is used by Lubuntu or XFCE all of which all much lighter and faster. I myself run Gnome3 which is in between and should run fine on your system.
You install any of these from the Ubuntu software center, just search for desktops and can select them during boot by clicking on the little Ubuntu icon next to username during sign in or if you have auto login set you just logout and make your selection and log back in. It will always boot to the last one used.