Which branches of chemistry and in what order to learn (self study)?
I agree with LDC3 that inorganic chemistry should definitely be your starting point; it builds foundations that apply to all of chemistry, which is why they teach it first; organic chemistry is just a branch, albeit a very large one, of chemistry that can also be very interesting once you know the fundamentals. Unfortunately using conventional textbooks etc, you will most likely be constricted to this order of learning, because of the level of these courses in the education system, where inorganic chemistry is very traditionally taught first, with organic chemistry only afterwards.


  Any short-cuts would be greatly appreciated - I basically just want to get to a point where I can read a wikipedia page on neurotransmitter X, psychoactive Y, or food ingredient Z and be able to comprehend fully what is going on.


I don't know if there are any shortcuts that you are seeking, Wikipedia can be pretty advanced because it is (usually) written by experts who know exactly what they're talking about; and especially on those high-level concepts, there are a lot of "things" (for lack of a better word) that you have to already know to understand fully what the big picture is. Trying to pick and choose would be maybe even more time-consuming than learning things in a progressive order.

Even though this sounds pessimistic, learning chemistry can be rewarding if you work at it, not to mention you have this site and tons of other online resources to help you out along the way.

-Best of luck should you choose to continue, and I hope you do!