As a NC diver with most of my dives off of our coast, I can tell you that it is some of the best diving in the world (and I've dove Little Cayman, Hawaii, Curacao, and others). I can also tell you that it is VERY different than quarry diving. Here are some tips you may want to consider since this will be your first ocean trip:
(1) Some folks who do a lot of quarry or shore diving are accustomed to bringing their gear in huge (sometimes multiple huge) containers. There simply isn't room for this on most boats. Take only what you need, pack it as efficiently as possible, and try to use a soft or mesh bag (as opposed to a hard-sided or Rubbermaid-type container) as these are much easier to stow out of the way on a boat.
(2) Unlike with quarry diving, you will be suiting up on a rocking boat with not a lot of room to yourself. Set up as much of your gear as possible on the dock (or on the boat before departure). On most boats this is required policy anyway, but even it if isn't do it anyway - it will make life much easier for you and everyone else on the boat.
(3) If you are prone to seasickness (or if you don't know if you are prone to seasickness) pick up some ginger gum. Around here they sell it at most grocery stores in the same area that you would fine the Dramamine, Bonine, and other anti-nausea materials. Unlike Dramamine, Bonine, or other medication, however, the gum will ease your seasickness without the drowsiness.
(4) Find out which operator will be running the charter(s) you are on and visit their website. You want to do this for at least 2 practical reasons: first, you can look at the boat and get a feel for whether you will be entering the water with a giant stride off the back or whether you will be rolling backwards off the side, so that you can practice the correct type of entry at your quarry (and if you can't tell, just call the dive operator and ask); second, we typically use a set up called a "Carolina Rig" that consists of a 10-15' hang bar under the boat and a system of lines that run you from the boat to the wreck, and most operators have a diagram of the system on their website so that you can become familiar with the system (here is an example from the great folks at Tortuga Charters in Morehead City -
Carolina Anchor Line Rig | tortugacharters.net). A word of caution - it is not uncommon to "go in negative" on a backwards roll, meaning that you go in without an inflated BC so that you start dropping immediately and can get to the hang bar before the current takes you away from it. I mention this only because it is a very different water entry than most people are accustomed to using and may be something you want to try at your quarry if you have a platform or other slightly elevated entry point available.
(5) Once you are in the water, the biggest difference from the diving you are accustomed to doing is the current. SWFTD has already commented on this, so I won't belabor the point other than to say that you should be aware of it and remember that it will effect your air consumption.
(6) You will (or at least should!) come back up the same set of lines that got you down to the wreck. After your safety stop on the hang bar, there will (or, again, at least should) be a "tag line" running on the surface from the back of the boat. When you ascend from the hang bar you will grab this line and pull yourself to the boat. A couple of tips here. First, be very careful getting back on to the boat, as a bouncing boat ladder is essentially a weapon! Just take your time, and make sure you have a solid grip on the ladder with out-streched arms before you putting your head too close to it. Second, keep your regulator in your mouth until you are completely back on the boat; you do not want to fall off the ladder without a regulator.
(7) In terms of gear, I would suggest adding 2 items in particular. The first is a wreck reel. I carry both a large primary reel with 350' or so of line, and also a safety reel with 150' or so of line. Some of the wrecks off our coast are largely intact and easy to navigate, while others are not and can be disorienting. A wreck reel will give you and your buddy the confidence to explore the wreck site while having a line back to the anchor. It goes without saying that you should practice laying out and reeling in line in the quarry prior to your trip
Second, and most importantly, invest in a "safety sausage", "see-me float", surface marker buoy (SMB), or whatever 40 other names they go by. I suggest a 10' version. Yes, it is a little more bulky than the 4' or 5' versions, but the purpose of a SMB is to be seen on the surface in an open ocean if you surface away from the boat and are drifting away. If you consider that part of the SMB is going to be underwater to begin with, a 4' or 5' SMB does not give you much visual aid if you are in 4' seas. With a 10' version, you have a much better likelihood of being seen. They are available for a very reasonable price ($59.99) from DiveProDiveGear (listed as the 10Ft. Open Ocean Cordura Signal Tube), but are also marketed by others.
(8) Bring tip money. The mates work very hard and usually only for tips.
My apologies for the length of this post, but I have tried to include the things I would want to know if I was preparing for my first dive off our coast. I think just by starting this thread you are already off to a great start - you recognize that being "advanced" certified does not mean that you are ready for every type of diving and are willing to take advice from folks with a little more experience in this particular type of diving. Trust your dive buddy, trust your dive skills, and most of all, HAVE FUN. Between the world-class wreck diving and big animals (our sandtiger sharks are a friendly bunch!), you are headed for a great dive adventure. I hope you guys and gals have a great time.