OK, this is as far along as I have ever gotten.
I have a mostly functional system on the home desktop, and am about to compile it for the laptop, although I'm still not sure if the wireless networking will work.
It is a home-built system, no binaries used, all the software running here was compiled on this machine itself. See http://www.linuxfromscratch.org/. The instructions for the basic system (called "Linux From Scratch") work pretty well, although some customisation of the kernel, depending on your particular hardware, seems inevitable. The instructions for additional software to be added to the system (called "Beyond Linux From Scratch") - that's a different story. This project has not been actively maintained, and the current version of BLFS corresponds to LFS five versions ago. Under LFS 6.8 (the current version), a lot of the BLFS packages won't even compile. Getting past that required (and still requires, since I need to install more packages) a lot of effort.
I have KDE 3.5.10 working, which provides a windowing environment. The web browser (which I am using right now) seems really clunky, I'll have to look at alternatives. I also have TeXLive working, so I can produce nice looking documents. I just can't look at them - the fonts on this system are awful. I really need to work on that.
Then I need to get Thunderbird and OpenOffice working. If I can manage that, I will have a system that does what I need it to do maybe 80% of the time. I'll have to work on the other 20%.
We'll see how this goes . . .