Well, my colleagues have said almost everything. Let me add one more fact, which is perhaps an important one. You say that individual differences can be very different; truer words were never said. My experience, after more than 50 years of language learning, is that individual differences are much larger than language differences. By at least an order of magnitude.I find, for instance, that, given the choice, I prefer to speak a highly inflected language like Spanish rather than an analytic one like English; even though my English is native and my Spanish pretty rusty by now, Spanish feels better to me than English, and so does any other language with a lot of inflection. My speech centers seem to be designed with synthesis rather than analysis in mind. And my bugbear in language learning is always vocabulary; grammar is a piece of cake, and pronunciation even easier. That's probably one of the reasons I became a linguist in the first place; so you might take all this advice from linguists with that piece of salt.
What I call "the linguists' disease" manifests itself, among other things, in learning to speak a language faster than learning to understand it, which is the opposite of what most language learners experience. Like Jim Fidelholtz, I can speak reasonably good German but get lost understanding it after a very few sentences. As I put it, I can usually figure out a way to get myself from point A to point B, but the native speaker usually returns by the scenic route, while I get lost.
That's just me (and some other linguists I know), though. There are lots of other people, and kinds of people, in the world, and there are probably about as many individual ways to approach second language learning. Any time somebody tells you something about the way "people" learn second languages, put your hand on your wallet, as Jim McCawley used to say, and ask them which people they're talking about.
-John Lawler http://www.umich.edu/~jlawler
"Whenever you hear a linguist use the word "theory",
you should put your hand on your wallet."
- James D. McCawley