I recommend the Wester Digital Passport in the 2TB size for you, but my favorite is currently the 4TB. I'm thinking of getting a 5TB so that 100% of the Wii & GameCube titles will fit, but the 4TB fits 99% of the games if you skip having all the different games versions and a few of the sing along games. It might not be needed, but I always use a Y-Cable with it to ensure proper power to the drive at all times.
I only use Western Digital drives and have never had a problem, well once I determined how they had to be setup. For a 2TB you'd only have to change the GPT partition format to MBR, format it to FAT32 32k and then everything should be a breeze. Anything larger and you'll have to do a little extra work and I'd recommend following the link at the bottom of my signature to set it up.
I've modded a lot of Wiis over the years and have used external WD My Book drives from the beginning: 1, 2, 3, 4, 6, 8 & 10TB. Like I said, after all of this my new favorite is the WD Passport 4TB. I like being able to color match the passport drive to the Wii (except that stupid blue color doesn't have a match).