If you got to the Apple icon in the menu (upper left corner), click on “About this Mac,” and it will tell you the version of OS you are running.
Couple of generic tips - run Disk Utility, and repair permissions. Also download Yasu or Cocktail and run those housekeeping tasks - especially if you turn your computer off at night.
When you restart your Mac, hold down P, R, option, and command (apple key) simultaneously and hold until you hear it chime a few times. Zapping the PRAM often remedies “weirdness” on Macs.
Another great utility to download is Applejack. You can find it on Versiontracker. You then run the program in single-user mode (hold down command-s when you restart) and it does a lot of the cleaning stuff before the OS boots.
I use Safari exclusively on my G4 tower and my PowerBook G4 exclusively 'cos Onyx and Firefox are dogs on my system, for some reason…
Also, how much memory do you have? Memory (or lack thereof) is a major culprit with the spinning beach ball of death (SBBOD).