Keep in mind Linux is expanding in capabilities just like Windows. While Linux will typically run on much older hardware, if you do a standard install of Linux from a typical Desktop distribution such as Ubuntu, Debian, Fedora, or Suse, for best performance the Hardware should be similar to what you would use to run Windows XP.
For older hardware from the Windows 95/98 era (or older), Linux can work on that hardware as well, pretty decent with a Graphical user interface, but you should use a light weight Desktop Environment such as XFCE, Fluxbox, etc.. for best performance.
You said you installed Ubuntu, while Xubuntu might be a better choice for that older hardware. Xubuntu is Ubuntu with XFCE instead of Gnome for the desktop. I know, I know, you probably don't know what any of that means just yet.. but now that you've heard it you can search around a bit to learn more about the choices available.
Distributions for Old computer hardware
Distributions with XFCE for a window manager
Some distributions have install discs that will setup XFCE during install so you don't have to worry about making the changes to the system. xubuntu
and the Debian XFCE Install CD1
is also mentioned quite frequently for working well on low spec hardware, it also uses XFCE as the default desktop.
So many choices.. and all of them free.