Alice- You've received good advice here already. Allow me to add one further suggestion:
Don't do this.
Your computer is pretty long in the tooth. $85 is not a lot of money, but it's still $85 that could go toward a replacement MacBook or MacBook Pro or some other Mac. It doesn't have to be a new one, but unless you absolutely have to run old Classic applications (very unlikely in 2011), then that $85 would be better as a starting deposit in a savings account that you'll add to until you can afford a decent used Mac with a Core2Duo Intel processor or better.
If you want to stick with your current computer, for whatever reason, then consider purchasing Leopard (10.5) instead of Tiger (10.4) as long as you don't need to run Classic applications. You should be able to get 2gb of RAM into that machine, and with Tiger or Leopard it will run much better with that second gig.
10.3.9 is not the worst OS in the world - I'd rather use it than any Windows OS. It's a very good choice for your current computer, as long as you run a decent web browser and keep it maintained (via Disk Utility) and updated (via Software Update). Upgrading the OS (and the RAM) might be a good option, but the limitation on "new" software you can run will be bounded by the hardware, not the OS, because it uses a PowerPC processor rather than an Intel processor.