I hadn't heard of K-Melon, but I see it came out in 2000 and current version is 2010.
I like FF 1.5 because it is pretty functional and runs on a whole lot less memory than newer versions and can be used on old computers like a PIII. I've even run it quite successfully on 256K, although it takes 10 minutes to load. That said, it's not very old, having come out at the end of 2005. The only real downfall is that there is no version of flash for it, and of course some add-ons which you might need to get work done, are not available for that version any more. Anyway, you don't really need flash unless you live in the boonies like me where there are no over-the-air radio stations.