The answer depends on which "White iMac" you have. There are at least three broad families of iMacs that at some point had white cases. Please do "About this Mac" and see what that says about your processor and post it here. that should look something like this:

The second red arrow is where you will find your processor information. Please tell us what your computer shows there.
If this is a PowerPC Mac, this is the browser most of use still dinking with old Macs use:
http://www.floodgap.com/software/tenfourfox/
TenFourFox is a modified version of FireFox that lets old Macs use the web without sites saying the browser is unsupported due to being "too old." I use it on a G4 eMac running OS 10.5.
The only downside is that almost no web sites are optimized for PowerPC Macs any more. Therefor any page is a slow load but it will at least load. TenFourFox does not use plugins so you cannot view videos.
If "About this Mac" shows you have an Intel processor, we may need to do more looking for compatible browser.