Any one helping you may be handicapped by the fact that we probably do not know enough about how such an organization works and thus could easily recommend a solution that creates a working database but perhaps not one that works well for what you want it to do.
A single unified table of contact information, whether you call it "people", "personnel", "contacts" is certainly a good start as it allows you to set up a single table for recording the basic contact info for all students and faculty.
(e.g., which grad students and post-docs "belong" to which faculty members)
That would appear to need these basic relationships:
Faculty::__pkPeopleID = Roles::_fkFacultyID
Students::__pkPeopleID = Roles::_fkStudentID
Where Faculty and Student are both occurrences of your People data source table. A field in Roles can identify the nature of the relationship. ("Graduate", "Post-Do"c, etc.)
For an explanation of the notation that I am using, see the first post of: Common Forum Relationship and Field Notations Explained
Thanks for your amazingly quick response! I appreciate that I'm not giving all the intricacies of the relationships, and am happy to provide more. In brief, a faculty member can have multiple students and multiple post-docs, but each post-doc and each graduate student works under a single faculty member. Your notation makes sense to me. I'll take some time to digest your answer, and then probably (undoubtedly) return for followup questions. Thanks again.
Then you may not need the Roles table.
Faculty::__pkPeopleID = Students::_fkFacultyID
may be all that you need with "role" a field in the Students (People) table.