Software :: Mac OS 10.1.5 - Adequate Browser Compatible?

I have an older iMac at home (my first mac) that still runs great with 10.1.5. I sat down to clean up files and programs on the system over the weekend, blah blah, but I realized that it only has Internet Explorer 5.1, I haven't used that computer, nor IE in ages, and here on my Mac at work I use Firefox, which I love. IE 5.1 is slow, jumbled, and so on on my home Mac. I've tried downloading and installing Firefox 2.0 but I guess my OS is a little ancient for it because it didn't work. Any suggestions for an adequate browser that's compatible? I found somewhere that IE stopped providing updates for 10.1.5... was that correct? Is there not a mac update for 10.1.5? Also, do you have any suggestions to assist me in getting my iMac back to speed? Its still a great system, but is there something out there that'll help me clean it up a little? I researched a little on the net but found next to nothing. I'd much rather trust you guys.