For most file types, allowing people to read the file means they can download the file. For example, if it is a text file, and if other people can read the file, then they can save it; they can also copy and paste the file to a new text file, which is equivalent to downloading the file. The same is true for HTML files, image files, PDF files, Word files, etc.
It is possible to support your requirements for certain file types using DRM (Digital Rights Management). Usually these file types are e-books or other copy-righted files. DriveHQ offers general cloud storage / cloud IT service, sorry we don't support DRM directly.
Our group account service might solve your problem. You can create different folders for different users, then share different folders to different users with different permissions. This way, each user can only access the folder(s) you shared to him/her.
If you share images to other people, you can also set the permission to "Preview Only". This way, the other people can only preview the images. They cannot access or download the original images.