I've thought about this question a lot, and I know for a fact that the Pokemon world is the one I'd be the happiest in.
That said, I can see a few drawbacks. Since I live in house with more than ten pets in it in real life, then I know something about the mess that animals can make. My house is not clean, and having a Growlithe leave fiery poops all over the carpet would cause even more problems, much less where I'm gonna keep the Lapras, I can't afford no swimming pool.
Then again, I wouldn't have to worry much about finances, but I doubt those battles are as green as they seem from this side of the screen. But training wouldn't be to hard, seeing as pokemon seem to have much larger brains than the average, well, any animal really.
All these thoughts aside, the world portrayed in the Pokemon games is a paradise, where people are friendly and it's filled with magical creatures to befriend, and as corny as that is, who wouldn't want to live there?