I'm probably nearing a dozen of these Linux setups for computer illiterate friends and family. It was PCLinuxOS back in the day, Fedora LXDE for a while after that, and at this point I'm using Linux Mint Xfce.
I tend to think desktop environment is more important than the distro. Nobody I'm doing this work for cares about the eye-candy in a mainstream DE - whatever it is, I'll configure it to look as much like Windows as I can anyway (for familiarity). If it can do that well, and has no other major shortcomings, the deciding factor is speed. LXDE and Xfce both are configurable enough for everything to be in a familiar spot (I even screenshotted a WinXP taskbar at one point and used that and the start button as a skin in LXDE
), and they're both blazing fast. Their speed has gotten compliments all on its own, and at least once has kept an old system in use that wouldn't have been much good with Gnome or KDE, much less Windows.
If anyone has the resources to make everything everywhere Just Work (or as close as we're going to get), it's Canonical (Ubuntu). Personally I can't stand Canonical or Ubuntu (not invented here syndrome and bloat, respectively), but Linux Mint seems to keep most of Ubuntu's good points and discard most of its bad ones. It's also available with Xfce, which saves some trouble. I've done 4 or 5 Mint Xfce installs now (including two on my own computers), and everything has Just Worked to an impressive degree. I haven't even found downsides of any note. Full disclosure, my most-used machine is Arch with Openbox, but that's really a different OS with different goals entirely. My gaming machine is Mint Xfce, though.
Whenever I have had problems with these Linux installs of late, it has been with printers (daft things). Both a Lexmark and a Brother have failed to work, to an extent that that machine is still dual-booting for the sake of printing only. I've even tried LiveCDs of different distros, but with no luck. I will say that HP printers have always been bulletproof for me (n ~= 5). It takes extra drivers, but Mint makes the process painless. The difference is that HP drivers actually work, while with other brands it seems to be 50/50.
Post-install, I do make a quick pass through all config exposed to GUI, but that's really just attention to detail. The real process is to make sure all needed programs are installed (FF, OpenOffice, browser plugins, and ask the user about anything else that might be needed), set the panels up to look like Windows in position and content, and make desktop icons for the used programs. It might be good to make a desktop icon for shutdown and point it out to the user, because Mint isn't great about exposing that (not that any recent OS is
). I also try to arrange for the user to attempt some basic use while I'm still around, so I can answer any questions or sort out any remaining issues.