To start, I ended up getting extremely specific about this, so if you have a question, let me know.
So there are a couple things to consider. I've beens shooting with Nikon for 3-4 years and have handle most of the Nikon macro/micro lenses aside from the crop sensor ones. I've handled most of the higher end bodies as well just from shooting events with my friends.
So the first thing is Nikon has two classes for bodies. They have general consumer bodies which are the D3x00 and D5x00 series. These bodies do not have internal focus motors, so the lens has the autofocus motor in it (this is how all Canon lenses/bodies are). The Nikon prosumer/professional grade bodies have internal focus motors. This means older autofocus lenses from the late 80's up until today can be used. They are also compatible with all Nikon lenses made since 1977 and will meter (expose) properly with manual focus Nikon lenses. The prosumer body is generally the one that's cheaper in the long run since you will have access to a much larger range of lenses at will autofocus/meter. You may have to put up some extra money to start.
So for the money I would grab a d7000. It's general goes for $350 or so used give or take depending on where you buy it. If you buy from KEH, Robert's camera ect used, you will usually get a 2-6 month warranty on the body. The d7000 is extremely well built too. You will appreciate the build quality after holding a d5x00 or d3x00. Do note this is the body will depreciate in price much faster than your lenses will. So you want the better part of the money going towards a lens if possible. You will lose some of the video quality and megapixels due to the d7000 being an older body.
For the lens, you can grab either kit lens like the 18-55mm VRII for less than $100 or even the 18-55mm and the 55-200mm for $150. Here's an imported one for $100.
http://www.amazon.com/18-55mm-3-5-5...&qid=1460427765&sr=8-4&keywords=18-55mm+nikon
Note that if you get a imported body or less and a couple years down the road you find yourself needing to service it, Nikon USA will not touch the item what so ever if it was not bought through a certified US vendor. With something like the 18-55mm I wouldn't worry about it too much. They're pretty cheap and they'll cost more to fix than they are worth.
Now note the 18-55mm can only reproduce at 1:3.2 or so at closest focus (3.2 cm in real life would be 2cm on the sensor). The 55-200mm is ~1:4.5 (depends on version, but around 1:4.5). You'll need extension tubes to get better magnification. You can't get the dirt cheap ones either since these lenses don't have an aperture dial. So you're looking at $30-$50 for good extension tubes (you might find cheaper ones). If you have a lens with an aperture ring, you can basic $10 extension tubes.
Now if you just want to take photos of corals close up and perhaps later get a kit lens so you take photos of your wife and kids or vise versa, that's fine. I'd save up and get the Nikon 60mm micro AFD ($200+ used) or the Tokina 100mm 2.8($400 new). So spend roughly $450 now and save $200 or $400 to get a dedicated macro lens in a few months. Alternatively you could spend $550 now and get the 60mm Nikkor AFD lens and later sell the 60mm Nikkor and put that money towards to 100mm Tokina. The main difference between the 60mm and 100mm is reach.
Both the 60mm and 100mm will work with the D3300, but they will completely be manual focus. You will usually use manual focus when you're shooting macro or anything up close. For general purpose photos, those two lenses will only autofocus on a higher end body. The 60mm micro Nikkor is almost entirely metal and is built to last. The Tokina is built similarly and in my experience is a better lens than anything lens at around 100mm for the Nikon mount.
Adorama sells referbs for $410 with only a 90 day warranty through Nikon. (no lens)
The d3300 comes with a 1 year warranty new (I believe). (With 18-55mm VRII)
Here's my personal take on it. When I had to upgrade my dx body (had a d90 and got the d7000), I just found someone on craigslist who had bought it and rarely used it. I got the original box and accessories when I bought it, and you can often haggle the price further down. Just inspect the body to make sure it is working.
People go out and buy gear camera from Best Buy, Costco... and think that the highest priced one is the one they need and never end up using the camera that often. It sits on the shelf for a couple months. They end up selling it from half or less than what they bought it for. You come and snag it for a camera that's been lightly used for a fraction of the price and it doesn't have any issues.
My final thoughts: The D3300 is good for the price, but going to the D7000 or D7100 will save you more in the long run if you want to do macro or photography. You have a much larger choice of lenses to choose from. If you live near a large city, you can probably just go to a camera store and play with these bodies and see which you like.