Okay... fins. $45. You already know "snorkeling" fins can be used for diving.
I guess that leaves it to me to get into full foot vs. open foot. The difference between them is that full foot fins pull on over your feet, and open heel fins strap on over a wetsuit boot. If you're only going to be diving in warm water and don't mind being barefoot when you don't have your fins on, full foot fins might make sense, as they're usually cheaper and some folks say they give you the feeling of having more control of the fin. I wouldn't know. I like diving in cold local ocean water, and I sometimes dive from places that would not be much fun in bare feet. I like having boots on, so I'm an open heel fin guy. I suspect you are too, if you plan do be diving wrecks in NC.
If you were going to get a full foot fin though, I'd get the Mares Avanti Superchannel. I have the open heel version of the old Plana Avanti fins with no "Superchannel", and they flat-out rock. You might still be able to find them on eBay or something. They're my favorite fins, but these blow them away in the reviews I've read. They're on the high side of within budget at $49.95, but I can't stress enough that you'll probably love them... IF you want an open heel fin.
If you want an open heel, we're going to have to look for something different to keep costs down.
Oceanic Vector
got a "best buy" from Scuba Diving magazine, and in their tests they were good in thrust and slalom, and excellent for speed and efficiency. The price is reduced to $37.50, and you're probably not going to beat that for an open foot fin in your price range.
If you go with the Mares full foot fins and the mask and snorkel I recommended, you'll have bought (4.95+44.95+49.95) $99.85 worth of stuff. After the 10% discount, that's $89.86. If you post a bit and get a ten dollar gift card, you'll spend $79.86 which is $0.14 under your maximum tight budget.
With the Vector, the total would come to $87.40. That's $77.86 after your discount, and a mere $67.86 out of pocket if you use the gift card. That's pretty sweet... $2.14 less than your low end budget! Of course, you'll want to put some of those savings toward shipping, and a pair of wetsuit boots...
Good luck, and happy diving.