Like others have said, it's gonna be hard to get everything you're looking for.
Some general principles:
-be prepared to spend a higher portion of your income on rent than you're used to. Everything else *can* be cheap here. It won't be if you spend a lot of time eating in western restaurants or drinking in expat bars, but it can be.
-Hong Kong is full of 3-bedroom apartments. It's not full of studios and 1-bedrooms in the way that, say, NYC is. You can find apartments of any size but the 3-bedroom is the norm. People live with their families. Smaller apartments tend to be concentrated in areas with more non-locals, which means either the more expensive HK Island neighborhoods, or poorer areas with the cage apartments that, well, you don't want. So like, if you were coming with a family it'd be a no-brainer, live in the NT along the East Rail Line, but there just aren't many studios or 1 bedrooms here.
-No matter how good a deal seems, don't live in a place if it seems like a fire hazard.
-personal opinion: Sai Kung is overrated. Far from everything and only kinda interesting. The hiking and running are great but you can be find that in convenient areas too.