HOG vs. neural networks for person detection
Unfortunately, this remains a very challenging problem, that even state-of-the-art techniques find difficult to do accurately.  It's probably too hard for a high school project.

The closest work is probably on "pedestrian detection".  Do a search on Google Scholar, and you should find a bunch of research papers on this from the computer vision community.  However, the state-of-the-art techniques are complex, and even the best techniques aren't super accurate.

You should also read about "object detection", "object recognition", and related topics.  That will give you the basics of how to use machine learning (like neural networks) to recognize the location of objects in an image.  One standard technique is to crop out a small rectangle from the image, use your classifier to check it contains the object you're looking for (e.g., a person), and then repeat this for many crops of many different regions of the image -- this tells you the location of all people.  There are other approaches as well, based on regression to infer the location of the object.

You might find Stanford's CS231N useful for learning more about these techniques.

For your specific problem, doing this in the general case is probably too hard.  I'd advise you to look for a way to make the problem easier.  One way is to make the problem more constrained and place your cameras carefully to make the machine learning problem easier.

For instance, if the room is a lecture hall where everyone will be seated and facing the same direction, you could experiment with placing a camera that will see everyone from the front, and using facial detection to identify and count the number of faces in the image.  Or, you could place a video camera at each entrance and exit and use facial detection or other methods to try to recognize people when they are entering/leaving the room, and count the number who have entered and the number who have left.  This will probably be easier if you have two video cameras over each door: one on the outside pointing in, and one on the inside pointing out.  Or, you could experiment with entirely different sensors, such as a FLIR camera which can see in the infrared.  People are warm and glow in the FLIR wavelengths, which might make it easier to distinguish people from other elements of the scene.