If you really want to take control of what this set of users can do:
Create an app and add your dashboard to that app. Move it or clone it, as needed. Also move/clone any saved searches or other knowledge objects that this app depends upon. Set permissions for all the knowledge objects to read only.
Change the navigation for the app, so that the default page in the navigation is the dashboard. Remove everything else from the navigation. (Here is info on how to Build Navigation for your app.)
Create a role. Assign your new app as the default app for the role.
Go back to the app and set the app permissions to only read for the new role.
If you want to make things super-restrictive - go to all other apps and: either remove all permissions for the new role or set permissions to only read, as desired.
Add users to your super-restricted role.
If you want users in other roles to be able to see the dashboard (but nothing more), you can also give only read access to those roles as well. Remember that a user may have multiple roles.