Upgrade to 10.3.9.
You can run Safari, and a lot will still work with it, but you also need to install something like Pith Helmet, which seems to keep this old version of Safari working with a lot of sites.
You can also run Firefox 1.5 if you can find it. That version works well enough with YouTube and other video sites.
Regardless of what others say, 10.3.9 is still quite a usable System.
However, it might be worth upgrading to 10.4, IF that particular iMac can support it.