auto mode is usually great for basic shooting and starting out, but its much better use other modes when you understand them so you can more tailor the shot to what you want it to be like.. ..
after you learn about aperture i would suggest shooting in aperture priority mode, the camera will adjust shutter speed and ISO for you but you choose what aperture to shoot at. you may even want to start playing with aperture priority mode right away. just read as much as you can about it and if you get a good understanding of aperture you will already be ready to use that model
aperture has to do with depth of field and how much light the lens lets in.. a low f number like f/1.8 which is a wide aperture will make so only part of your image is in focus and the rest is blurred, it will also let the most light in. a high number like f/11 the lens is not open as much and allot more of the scene will be in focus but less light gets in the camera. now if what you shooting is really far away even at f 1.8 most things will be in focus. the closer you are and the less stuff you will have in focus.
1.8 is a very fast lens. yours lenses will not have that wide of aperture but that should give you a good idea how it works.
shutter speed, a fast shutter speed will stop motion. so if you shoot a photo of a helicopter with a fast shutter speed the blades will be stopped in the photo. you can also get some or allot of blade blur depending on how fast or slow your shutter speed is. shooting at night on a tripod you can use a long shutter speed and get images that almost look like day time if the shutter is open long enough..
ISO.. the lower the iso the cleaner the image, less noisy grain in the image but also like the camera is getting less light, in low lighting without a flash and a faster shutter speed you will need a higher ISO which can cause more grain, the D5200 does very well up to 6400 iso with out noticing much noise in the photo..
there are the basics.. in full auto mode those are the 3 settings you will be changing to get the kind of shot you want.
there are a bunch of other settings in the camera, i would suggest setting it up like it says to in this guide to start out with...
Nikon D5300 User's Guide and than start learning more about the 3 settings i told you the basicsa about..