Your experience thus far is far from normal. It definitely should not go
into sleep mode right away and the screen should be readable. Try turning
off the power saving features. Go to System, Preferences, Screensaver and
click on the Power Management button. However, it may not be sleep mode that
you are seeing but a graphics driver problem. It may be trying a graphics
mode, but it isn't working and then defaulting back to something low res
that should work but isn't.

Did you install from the Live CD? Did Ubuntu work fine in Live mode? Did you
try everything to make sure that it worked by running off the CD?

If your problems continue we will need to know more about your computer to
be able to help further. Make and model would be nice. Amount of RAM, drive
specifics and graphics card make would help. Someone is bound to have the
same computer as you and will be able to help troubleshoot your problem.
Please be patient.