Please read through some of the many threads here about starting locals. Some of them are harsh, but accurate nonetheless. The one thing you've got going for you is you're opening to calling yourself a club.
Are you intent on being a local? Do you mean Zeta Phi Beta is the only NPHC sorority represented or the only sorority period? Is there a reason why you aren't interested in Zeta? Is the campus in a position to desire expansion, whether it be a local or national sorority? Do you have a campus Panhellenic?
Regarding the letters, try researching NPC, NPHC, NIC, service fraternities, multi-cultural sororities, professional fraternities, etc. There are a gazillion of them out there. Typically the letters stand for something other than copyright or creative infringement from a popular movie.
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