Cool birthday gift.
I get seasick if I am not careful. If I keep my eyes on the horizon I am OK - so I spend any time when the boat is moving significantly outside or inside in a place where I can see outside and then I don't need to take drugs to avoid it.
Have not been on the Aggressor, but have been on the Peter Hughes boat. Very similar boats, you will see it parked directly beside the Aggressor when you board.
In open water the boat will pitch a bit, but these are pretty large boats so not so much unless the weather is really bad. They really roll however if there is any weather at all. Moving between sites in the day time I was unable to stay below decks or inside at all. I take drugs to knock me out if I need to be in bed asleep while the ship is moving. At night the PH boat moves to a protected site so there is virtually no movement during the week while you are sleeping. Aggressor probably does the same.
I found that for most of the dive sites the water was protected so there was very little movement when getting ready for a dive. This depends on the weather and the site - if the waves and weather are coming from the same direction or it is calm - the boat is very stable. If they are coming from two different quarters the boat will roll quite a bit and those who get seasick will be uncomfortable. Mostly this will be the sites on the east side of half moon cay. Probably won't even do these sites if the weather is bad so I wouldn't worry too much.
I take three wetsuits, 5 bathing suits, 7 t-shirts, one pair of shorts and clothes to get there and back. Take my shoes off when I get on the boat and don't put them on again until leaving a week later. Barefoot the entire time. First trip I didn't use most of what I brought so I have pared it down considerably. I change into a fresh bathing suit after each dive and wear it as shorts until the next dive - rinse the one you just used and hang it up to dry. You might want a pair of light kakis for dinner to dress up a bit, but not necessary.
Three wetsuits is perhaps overkill, but always having a dry one is very nice and two of them are shorties so not putting on a wet one keeps me much warmer. I use the 2/3 full suit for night dives or when I feel I am getting cold. Lots use 3 mil full suits all the time and two would be a good idea otherwise you are always getting into a wet wetsuit so you lose the benefit of the added neoprene warming up the water in the suit. (This depends on the outside temperature, I was there in December so it was not hot, just warm with regular showers and cloudy periods.)
Hope that adds to what others have said.