I don't know diddly squat about the history of Fraternities, but when it comes to sororities, there is always going to be some kind of debate as to which organization is the oldest.

This info was obtained by using the SEARCH FUNCTION:

Alpha Delta Pi (started out as Adelphian Society): 1851--the first secret society for women

Phi Mu (started out as Philomathean Society): 1852

Kappa Alpha Theta (the first to be FOUNDED with a Greek name): 1870

Gamma Phi Beta (the first Greek letter women's organization to call themselves a SORORITY): 1872--the name SORORITY was coined especially for them by Professor Frank Smalley of Syracuse University. This is what the GPhiB website states: "Eight years after their first meeting, two members of the Alpha chapter went to the University of Michigan to charter the Beta chapter. Upon their return to Syracuse, Professor Frank Smalley commented, "I presume that you young women are now members of a sorority." Thus, Gamma Phi Beta became the first women’s fraternity to be called a sorority."

Even with this information, people are still going to claim "so and so was REALLY first because...." so the debate still goes on.

There are numerous threads here on GC that may assist you on your project and I'm sure that some of the organization websites may be able to help also.