There's a few ways to to go about this....
1. For any Wii content (games, gamecube games via Nintendont.etc) you could just install these as Wii U forwarders. This means you can have a single USB HDD, formatted to WBFS (Wii U filesystem) and install all of your Wii U and Wii games and launch them all from the Wii U menu.
Honestly that's my preferred way as the end result just feels more like individual games, and not just a pack of .iso files you run from some launcher. Yes, it does mean you cannot just copy/paste that huge pack of Wii games you found on some torrent site, instead you will need to install each one using something like NUSSpli or WupinstallerGX. You can also create your own forwarders with something like
TeconmoonWiiVCInjector.
One downside to option 1 is you are then limited to a maximum of 300 installed titles as there's no appetite in the Wii U community to ever patch this. You will likely run out of titles before you run out of storage.
2. Partition the HDD as per the
excellent tutorial written by SDIO.
3. You could use 2 Hard Drives, really these should be SSD's otherwise you will consume all 4 USB 2.0 ports with Y-Splitter cables. One formatted as WBFS (so shows up on the Wii U), then the other formatted for use with the Wii. Option 2 makes more sense than doing this I think.