Looks like you did a decent job for a first timer. A lot of people are completely lost on the first time stuff.
I know I'm in the minority with how I work with deer when I'm lucky enough to get one, and it's been a few years but my simplified process is this -
I don't field dress a deer unless it's an extremely massive animal that I know I can't haul out of the woods by myself without trouble, or if I am too far into the woods and don't feel like adding dead weight. Anything under 140lbs or so does not get gutted. I do this because I feel it keeps the meat cleaner and you don't accumulate dirt, debris, rocks, etc on your drag out inside the carcass. Remember, that warm, moist body cavity is a fertile ground for bacteria, and when you have gunk from the woods falling into it, you are just adding fuel to the fire.
Once I get home, I hang the animal from a gambrel from the back hocks. I make a cut around the skin just above the hocks (don't cut the tendons, those tendons are what holds tension to keep the deer up.) and then make a cut from each hock down along the butt of the deer where the white hair meets the brown hair, down through the anus and back up the other leg. If you ever saw a trapper skin an animal, it's the same idea - "cased" cut. Cut through the tailbone and cut the genitals off UNDER the skin and start peeling the hide down. This is best done while the animal is still warm. The longer the animal sits, the harder it will be to skin.
Cut the forelegs off at the "elbow" joint with a hacksaw. If you are not saving the cape for a taxidermist, you can also cut the head off at the neck/skull junction with a saw at this point. If you are saving it, that's a whole 'nother ballgame for skinning and for the intent of this being a meat deer thread, I am not going to get into it.
Peel the skin down, and once you reach the belly area, be careful about your cuts, don't puncture the internal organs. Usually the skin will peel down off this area with no problems while it's warm. Continue working the hide down over the forelegs and then down over the neck. If you did it right you should have a deer skin that looks something like a tubesock.
Once the skin is off the deer, I put a trashcan underneath it with a heavy contractor bag inside of it and unzip the stomach cavity and let gravity do it's work with the guts. Saw open the ribcage so you have easier access to the chest organs. Immediately after all the guts are in the trashcan, I hose the entire deer down, top to bottom, paying particular attention to the body cavity. Spray off the hair, blood clots, gunk, and get it looking nice and clean. Any stray hairs remaining can be wiped off with a CLEAN rag (get a bag of cheap ones that you can toss afterward.)
I cut off the forelegs first at the body joint and then throw them in a cooler of ice. Then I remove the inner tenderloins "preacher's meat", and back straps and set them aside.
At this point, I then cut around the pelvis, using the bone as the guide, on the back legs and work my way down to the ball and socket joint and detach the hind legs from the main carcass. It helps to have two people at this point, someone to hold onto the main carcass so it doesn't hit the ground. Cut the remaining leg off at the hock and put the hams aside in an ice cooler.
Lay the carcass down on a table, at this point I remove the ribs and strip any big pieces of flesh still on the carcass for burger meat. It's up to your judgement on how picked clean you want to go, but I usually am one of those people who will make it look like vultures had at it and remove everything I think is useable.
I then wrap and freeze the back leg hams and take them to a processor to be sliced into steaks. I cut down the meat from the forelegs and neck and it all goes into the "burger meat/jerky meat buckets." I cut the backstraps in half for a total of 4 pieces and freeze them separately. The real work is in the separating the silverskin from meat you've removed and not the actually skinning/butchering itself. From this point on, over the next day or so, my focus is just to prepare everything I've separated for burger or jerky meat by doing just that.
I've gotten fancy in the past and cut steaks and chops and all other sorts of nonsense over the years out of the back legs, but at this point I'd just rather freeze them and have them sliced into ham steaks.
Also, when it comes to freezing, a vaccuum sealer is nice, but not necessary. Just wrap up the meat well in several good layers of plastic bags and keep the air out. It also helps to invest in a freezer that is NOT frost free. Frost free freezers basically act as a slow freeze dry machine and that's why you get freezer burnt food.
