Debian is one of the first distributions used with linux-wiiu, and is one of the more mature distros on offer for powerpc platforms. Currently it's not officially supported on powerpc, instead with untested packages being supplied by the "Debian Ports" project. Despite this, it works well on Wii U.
[TODO. should be debian/tarball-specifics, will make single page for flashing images]
Once the console boots up, login with user root and password wiiu. You should immediately get asked to change the password - pick something good! A normal user account, wiiu, also exists with the same password.
Once you're in, you'll need to finish setting up the system to your liking. Since Debian attempts to set the clock from the Internet, you should have the correct timezone:
After that, you may wish to adjust the keyboard layout or font size (the default is pretty big, to help TV users):
dpkg-reconfigure keyboard-configuration dpkg-reconfigure console-setup
If you choose a generic 105-key keyboard and are only shown English (US) layouts, you should find an "Other" option at the end of the list. If asked about console encoding, UTF-8 is a good choice, or ISO-8859-15.
You might want to give the wiiu user access to sudo, so you don't have to log out to do administrative tasks:
usermod -aG sudo wiiu
At this point, it's probably a good idea to log in as wiiu to change the password:
su wiiu # [password change nonsense...] exit
[TODO: get internet connection]
Optional: Graphical Desktop Environment
Most people like to have a GUI, which is fair! Check out Debian's list of supported desktop environments. XFCE, LXDE, LXQt, and MATE all work well on Wii U. Keep in mind that, at the time of writing, there's no GPU support in the kernel, so a heavy desktop like Plasma will run poorly or may not run at all.
Look through each desktop's Debian Wiki page for installation options. Generally, where a task-<something>-desktop package is provided, this is your best bet for a painless install - though you will get a 'lot' of extras!
An example for MATE:
apt-get update apt-get install task-mate-desktop