Epic Mickey 3DS takes place directly after Epic Mickey 2, which in itself is a sequel to Epic Mickey. I guess I would either: Go ahead and play it and let us know, or 2: see if you can play one and 2 before jumping into the 3DS console.
I played the demo and it seemed pretty straight forward to me. I was pretty caught up to speed just reading previews and reviews of the original Epic Mickey. I think Power of Illusion has just as much to do with the Castle of Illusion game on the Genesis as it does with the original Epic Mickey on the Wii. In other words if you want to play the 3DS version I doubt you would have to play the original game to understand what is going on.
I've never played any of the other Epic Mickey games but I was able to appreciate the game as a standalone title.It's a fairly simple storyline that can be understood on its own without prior knowledge of the series. I'm sure there might be some slight nods to the past games (such as Mizrabel being the villain in the Genesis title Castle of Illusion) but as long as you have a love for the Disney universe and its characters, I think you'll enjoy the game.