Nikon D3300 for coins?

No, just the D810. The older models don't have the electronic shutter, at least not without hacking the camera firmware.

This is true. Here's a comparison pic, 100% crop from the "8" in an 1883 Dollar, I took after I replaced my D7000 with a T2i:

 

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I use to use a Canon T3i but recently upgraded to the T6i and got the 100mm Macro lens. Total cost of the new set up, $1,100. Not cheap but I use my camera for other things than coins.

I want to buy a copy stand but funds are being spent elsewhere at the time.

 

Nothing I could sell you on, short of a $2000 Printing-Nikkor 105mm, will exceed the capabilities of that combination. It's good enough, in fact, for you to forego the complexity of tethering if you wish. I've owned 4 different examples of that lens and all have autofocused and shot flawlessly even through a slab, when you set the camera to Spot metering and the focus point to the center of the coin. It's just a terrific lens. And if the working distance is acceptable to you, there's nothing on the market better as a portrait lens.

Tethering still makes things easier, but you will almost certainly not find it necessary to manually focus this lens.

 

Yes he tethering is very nice. I think robec told me about that. That manual is way too big to read cover to cover!