What is the general way to find the "connotative meanings" of a phrase?
I am guessing that some voting website will do the work.
I am not sure of a website for such a thing, but the phrase "hand-picked" usually has positive connotations. It suggests that who- or whatever was chosen was selected with much thought and research going into that decision, often the "cream of the crop" so to speak. For example, the President of the USA hand-picks his cabinet members as the top-performers in their respective fields (ideally).