... I just want to be able to run all/most of the website,programs etc. on the web today.
Even though it is a Mac that is a lot to ask of a ten+ year old computer. Most websites, sure, but YouTube, streaming video, anything demanding of your CPU... not so much.
You will need to specify a lower resolution, say 240p, for Flash video to be reasonably watchable. I got the most longevity out of my 1 GHz G4 Powerbook by installing ClickToFlash which prevents resource-gobbling Flash advertisements.
My 1.67 GHz Powerbook does better.
This is your PB - PowerBook G4 1.67GHz 15" The speed is barely fast enough. You need to max the RAM to 2GB. How much do you currently have?
Flash Player version 10.1.102.64 is the last version available to PPC Mac users. However, this Flash version won't work for many videos on Facebook, YouTube and other sites. Adobe's latest version, 10.2.x or later, is only for Intel Macs. Adobe will not provide a newer Flash version for PPC Macs.
The message requesting that you download Adobe Flash Player takes you to Flash Player requiring an Intel processor. Doesn't work on a PowerPC processor. I found a hack, installed it & it works with Firefox, TenFourFox & Safari.
Download this http://www.steelbin.com/FPforFBPPC.zip to your desktop, unzip it, and replace the current Flash Player plug-in which is in your main/Library/Internet Plug-Ins folder, (not the user Library). Save the old one just in case this one doesn't work.