The most direct way that I can answer your questions is to say that I would feel safe if it were my family living in the Van Vorst Park neighborhood. I have friends with children that live in the area and they couldn't be happier.
I would feel comfortable investing in a primary residence in this and other areas of downtown Jersey City. There are certainly more tertiary areas outside of downtown Jersey City that I would advise against.
I would further clarify that Van Vorst is not in transition and that the core of the neighborhood is very stable. However, there are plans for expansion in areas adjacent to Van Vorst namely Liberty Harbor. This expansion along the Morris canal is a phased development over the next several years and does not threaten the stability of the surrounding area but will serve to provide more amenities and points of interest that add value to the community.
You should come and visit the neighborhood, my office is just 1 block from the park. I think you'll like what you see and I'd be happy to show you around.