With regard to the D5300 and macro, there are several options depending on how much you want to spend, and how seriously you intend to worry about some of the finer points of image quality.
The 40 mm. lens mentioned above has a good reputation as a sharp lens, reasonably fast, and its focal length is such that it makes a very good normal lens. If you don't already have a normal length prime lens, this might be a very good choice, even though its macro capabilities are less than ideal. The closeness to objects makes nature macro difficult, though not impossible, and also can compromise lighting. But these things can be lived with, and remember too that many shots will be close up but not truly macro, and for those 40 is not so bad. If you want, for example, a whole butterfly on a flower head, you won't need to get all the way in.
There are other macro lenses,of course, which are more expensive. That one is pretty affordable, and versatile.
A very cheap alternative that can work well within limits is a diopter lens. Mounted to the end of a normal lens like a filter, these range from fairly expensive and high quality to very cheap and poor quality. These lenses tend to introduce some distortion and to be soft at the edges, but for many uses that does not matter. You don't need perfect linearity for a bug, and most of the time the edges aren't in focus anyway. The advantage of these lenses is that they are cheap, easily carried, and that the don't interfere with metering or auto focus. Raynox makes a clip on one that's fairly decent in quality and fits various sized lenses. Other makers make screw in ones, often in sets. Consider something like this as a starter, because even if you go to something else later, you can throw one in your bag when you're traveling.
Extension tubes and bellows used to be very common macro accessories, but are less so now that lenses need electronic communication to work right. An extension tube goes between the lens and camera, and effectively makes it a macro. You lose some light, but a good lens on a tube works very well, and this allows you to use a non-macro lens closer up. Some tubes used to come in sets of varying length that could be stacked for different combinations. Included in this general class are lens reversal rings, too. On a tube or bellows, or even alone, you can get a mount that turns the outer end of a lens into a bayonet for mounting. Reversed lenses can provide very good linear macro. But the operation of a reversed lens is 100 percent manual.
If you are willing to go entirely manual, the D5300 will accept just about anything with a Nikon mount, including old uncoupled extension tubes, manual lenses, reversers, etc. You'll get a no-lens error in any mode but M, and no metering, but you can use the post-shot histogram to correct metering errors. ON a D3200, I've used all sorts of odd things, including a microscope mount with typesetting lenses, old pre-AI telephotos with a stack of extension tubes, a bellows, and so forth. If you are willing to go all manual, you might check out older macro lenses such as the 55/3.5 micro, which, while suffering a bit from the distance problem of the 40, is often dirt cheap, and eye-slicingly sharp.
The one thing you can't readily do on this camera is to use one of the AFG lenses in reverse, or with a non-electronic extension, because the aperture will close down completely. If you want to reverse mount the kit lens you'll have to manually jam the aperture actuation lever, not really recommended. You're better off finding an old lens with an aperture ring.
Just for grins, here's a macro I did a couple of years ago with a D3200 and a compugraphic typesetting lens (no aperture, no meter, no focus except to move the camera).
