1. Six of one, half dozen of the other (meaning no real difference). One's pre-packaged by the manufacturer with a controller (enclosure) and a drive already installed. The other is a roll your own situation. To be absolutely clear, the real concern is ALWAYS the controller --- that's what makes or breaks it with the Wii in mind (nine times out of ten, it's the determining factor as to compatibility). You'll have far less issues with USB 2.0 than 3.0.
I use a Western Digital combo that's well-known to work (they revamped it later with 3.0 and I can't speak as to that). You want cheap and compatible? Buy this for $8 and find a 2.5" SATA drive to put inside it. I bought one for my sister and the Wii I gave her, works well.
3. Wiis are limited to 2TB, last I knew. I'm not for certain if some kludge exists for larger drives.