Hey Aaron,
I enjoyed your post, I have a couple thoughts that will hopefully be helpful. I currently own two one beds, located in Carroll Gardens and Park Slope, I also own a 3 bed in South Slope that I live in.
In regards to the four neighborhoods you mentioned and how they will potentially appreciate, I would say the following:
PLG- I wouldn't buy a one bed unit here, as it primarily attracts families looking for relatively affordable singe family town houses, and doesn't offer much that young professionals would be attracted to.
Prospect Heights- A great area full of dinning options, transportation, bars, etc. Very desirable, but largely already mostly discovered, would be hard to find a deal.
Park Slope- Probably the most blue chip neighborhood in Brooklyn, incredibly stable, will most likely continue to appreciate at a modest rate. I would liken buying a unit here to investing in Microsoft or Apple stock.
Prospect Park South- To me, this is the most undervalued of the areas you mentioned and has the greatest future upside potential. Pretty good transportation options, tons of cafes, etc. Being close to Prospect Park will always be valuable.
Hope this helps, feel free to reach out to me privately if you would like to talk in more detail. I could give more accurate insights if I knew ballpark budget, if it's for yourself or to rent out, etc. Either way, best of luck, no matter what you buy in BK you will win over time.