Hello Kithy,
OS9 and Internet Explorer will work just fine with Verizon's DSL; they may not be officially supported, and you may have gotten a techie unfamiliar with Macs or OS9. You should have the latest upgrade of IE which is 5.1.7 although the original install which I think is 4.5 should work. I just installed from an OS9 CD last night and I checked to see before I upgraded. You may have to search these posts or Google to find the download link for the latest version; it's no longer available from Microsoft.
I suspect you may be having other troubles installing.
iCab should work, too, and - although I don't use Mozilla myself - if Tom says it works you may take it to the bank.
If you decide to go to OSX (which I find more capable but less user-friendly), avoid 10.2 (Jaguar) and get either 10.3 (Panther)(my favourite) or 10.4 (Tiger). I got my copy of Panther from
http://Applerescue.com for $59.
In my experience, OSX browsers Safari, IE, and Firefox all work well, although there are some differences.
Good luck ..... Jon