Hi. I'm not sure what stage you are exactly at by your post. If you have *just* been approved then your approval is sent to NVC and then to the embassy in Cairo. Not sure what you mean by it being sent to NY, since there is no service center in NY.
Once NVC sends the approval papers to Cairo, Cairo will send to you a package 3. This package will have an instruction sheet telling you exactly what you need. I'm not sure if the K-1 people have a different set of instructions than the K-3 people so hopefully someone from Cairo with a K-1 will chime in.
After you have completed all of the papers that the instructions from the package 3 lists out, you send it back to the embassy. After the embassy processes the paperwork they will then send you your package 4 which basically just tells you what the date and time of your interview is.
So...................... you get your approval------->it's sent to NVC------------>NVC sends it to Cairo (about one week)---------------->Cairo sends you a packet 3 (hopefully one week from the time Cairo receives info, though people have been having problems receiving the packet 3)---------->you gather all of the info listed on packet 3 instruction list----> you send everything back to Cairo------------> Cairo sends you the interview date and time after processing your paperwork(averaging about 2 to 3 months from the time you send in the pact 3 to the time they send you an interview date)------------>go to interview------------>you are put on ap for security checks(anywhere from two months to eternity).
As for what to bring to the interview....again K-1's are different so hopefully someone who's recently been there can let you know.
Good luck!
oh and even if you haven't gotten any paperwork yet from the embassy I would start now gathering some of the info. The wait time to get the interview and to be put on security checks is long enough so you don't want to have to wait around for something you could have already done. For some reason my husband's military papers are taking a LONG time to get done. He's been at it for a while now and we have the pkt 3 and are STILL waiting for these stupid papers. He said it has to do with the fact that he's an only son and that he's never asked for this stuff before so they have to do research on it or something. Anyways you don't want the process to be waiting on you since it's gonna be waiting on the embassy and the Dept of State long enough!