You would do yourself a favor by finding another hunter in your area who is willing to help show you the ropes. Not everyone would do that, but if you can get in a club or connected to a seasoned hunter who'd take you under his wing, it will help shorten your learning curve big time.
I grew up not far from a slaughterhouse and knew how to dress a cow by the time I was 9 years old. Deer are just smaller versions of cattle really. The better care you take of dressing the animal the better the meat will be. I have seen guys who leave the guts in for hours, or drive the deer around in the back of their truck showing it off around town. That kind of thing will not improve the taste of the meat, believe me. I usually field dress a deer within 10-25 minutes of the shot. The longer waits are usually for a bow-shot deer that I had to wait on or had to look for. The quicker you can get the insides out and start cooling the meat down, the better it will be.
I have hunted a few places pretty deep in the woods that don't allow vehicle traffic where it only makes sense to gut them not far where they fall. There's no sense in dragging the added weight of guts if you don't have to. If you are goin to the trouble of hunting in deep woods, you're probably not going to shoot the first young buck you see, because it is a chore to get something that size out of the woods (especially by yourself). You probably wouldn't hunt such a place the next several days afterwards anyway and by the time you hunted there again, everything would have been cleaned up long ago.
I shot a buck way back in on some public land eighteen years ago at a little after 7am and it took me until a little after noon to drag him out by myself. He was the biggest buck in the area and I knew I wasn't going to be hunting that section of woods again for a time, so I gutted him where he fell. I accidentally left something in the woods by the stand site and had to return the following day. Everything but the stomach contents was gone.
I'll post a picture of him here.