I have a not so computer literate family member who wants to see what this whole linux thing is about but don't know whether to suggest Ubuntu or Slackware? Thoughts or suggestions?
As with any operating system, installation is the biggest hurdle, particularly if the user needs to preserve existing data. Once past that point, however, if he can handle Windows or OS X, he should have no trouble using and maintaining Ubuntu.
Once you're in your desktop environment, the biggest difference you'll see is that Slackware is more responsive and more stable. KDE 4.4 in particular has the non-technical user covered. XFCE is easy too, but you might want to add some packages (which Robby Workman always seems to compile and have available on his site). Oh, and you should install WICD from the extra folder on the DVD if you use wireless.
Slackware also has slackpkg in by default now. You have to do it at the command line, but it updates the official packages with two simple commands.
Updating to a new release is still not as easy as a lot of other distros, but that's one of the bullets that most probably should bite and reinstall from scratch once a year or so. And if you don't want to I'm sure a Slackware install will continue working at least as long as the Ubuntu LTS version.
The thing is, Slackware still gives you vanilla packages, but the advances throughout the system have made vanilla a whole lot richer.