Make certain you are allowed to do it "gutless" in your state before you do. Some states require you to check in the carcass. . with bones.
Try to keep it simple. You can go very nuts and very meticulous, and you can go quick and dirty with only a small pocket knife or even a broadhead if you forget your knife. It gets easier with every passing deer.
Whatever you do, get it home, get it clean, and get it cool. I hose mine out once I get home. Make certain to let it dry out after the hose, but you get any spilled "gunk" off the carcass and it helps keep it sanitary, as well as starting it on its way to chilling.
ChuckC