Wii U games still require a dedicated drive. Also note that if you get a USB hard drive, it will need a y-splitter cable to draw power from two USB ports since the Wii U doesn't usually give enough power over a single port. So, it's probably not a good idea to get two hard drives unless you don't plan on using the USB ports for anything else.
If you go the flash or SSD route, be aware that the Wii U will write to them even when the system is in standby. If you don't have standby mode enabled it's not as much of an issue, but even Nintendo recommends against using those types of storage due to the limited write cycles and the way the Wii U OS constantly writes to them.
Another option is to put your Wii and GC games on the SD card. I don't know if there's a significant difference in terms of read speeds between Wii and Wii U, but I've had no problems running both Wii and GC games from SD on my Wii U. Even the games with streamed and audio and video seemed to work fine. But don't take my word for this as I'm sure there are some games that could still have problems.