" is there a preferred order in which to do it?"
No. The three upgrades that you are doing are independent of each other. Although possibly the new Qt may need the new glibc. If so then install the new glibc first.
"And to install the ALSA driver for my sound card (to hopefully enable sound recording), according to Roderick Smith's book Linux Power Tools, the first thing I need to do is recompile my kernel."
When you recompile the kernel you should install the new kernel as a second kernel and dual boot the two kernels until the new kernel is stable.
"To install another application I am told that I need to install Qt libraries"
KDE and Qt are mutually interdependent. If you upgrade Qt then almost certainly you will have to upgrade KDE to the version compatible with your new Qt version.
"(And the documentation, at least for installing the glibc libraries, makes it pretty clear that something probably will go wrong (:-).)"
It is not so much that something will probably go wrong. It is the bad consequences of a botched glibc update. With a glibc update if something goes wrong then the vast majority of your programs stop working and it is hard to reverse your way out of the problem. So back up your system before you do it and have a way worked out to restore a non running system.
Given the age of your Linux system and the size of the changes you want to make I think you should give serious consideration to a complete install of a current Linux distribution. It would not be any more work and you will get everything upgraded to the latest version.
Be prepared. Create a LifeBoat CD.