In my opinion, the ordering is somewhat a matter of opinion, but here is how I feel you ought to go, and the progression (which I will be doing in stages over the next day or so).
In my opinion, this is the easiest of the lot, requiring little more than a bit of balance and the ability to hold your bodyweight above your head with straight arms. The progression is simple:
- Handstand with your legs on a chair or bed - Many people can skip this part, but it's important if you don't have enough arm strength to hold your bodyweight yet. With your feet on a bed, chair, or other raised platform of hip height or higher, hold yourself up in a handstand position. Try to get your torso vertical and everything from hips to chest to shoulders stacked over your hands.
- Handstand against a wall - This can be built up to from the prior step, elevating your feet higher in the air until they're practically vertical. A common method involves facing away from the wall, putting your hands on the ground, and "walking" your feet up the wall, adjusting your hands to get closer to the wall, until you're vertical. Alternately, you can put your hands on the ground and kick up into the handstand. The former is more controlled and less likely to damage interior walls. The latter will start teaching you to kick up into a handstand.
- Now, you're going to start kicking up into the handstand. This can be the scariest part for people because they're afraid of falling over and hurting themselves, particularly if their feet overbalance forwards. The best trick here is the one-handed handstand escape. If you're in a handstand, and you lift one hand, you will naturally rotate to land on your feet. That solves 90% of the problems, but I would also recommend starting on grass or carpet at first just in case you panic and forget. I have been taught two different ways to learn to go up into a handstand at the start and different people prefer one or the other. The first is to put one foot in front of the other, lean forward, put your hands on the ground, and kick up one leg while jumping up with the other, then trying to bring your feet together. You may notice that this is the same technique you may have used to kick up into the wall in the prior step. It's slightly unbalanced since one leg is going up first, but most people seem to find it easiest. The other is to start in a squat, put your hands on the ground, then lean forward and kick upwards into the handstand. Either way, your two main methods for maintaining your balance are leg position (try to get them above you, or slightly past your head, and you'll probably want to start with straight legs) and your hands (pushing with your fingers or the heel of your hand depending on which direction you're tipping). Really, from there, it's just a matter of continued practice.
Alternately, you could try Lucas's 5 minute tutorial on Youtube. I'm not affiliated with him, but I'm a fan of his work.
This is a fairly elementary skill, but one which does seriously tax your core pretty quickly. There really isn't a progression to follow for the most part. You just sit on the ground with your legs out, put your hands down, push down as far as you can, and then lift your legs for as long as you can. If you are truly finding that you can't lift them at all, you might try starting sitting on an elevated platform like a chair so that you can start with your legs at a greater angle than 90 degrees. You can also start by doing "tuck sits" where instead of lifting your legs straight, you bring your knees up to your chest. If you lack the core strength to lift your legs, start by doing hanging leg-lifts, first with your back against a wall (standing against a door and reaching up and grabbing the top is a good way to get here, although you will probably want to use a towel to prevent splinters) and then without that bracing in the back.
I'll admit that this is one that I haven't done, so I'm cribbing from Lucas's 5 minute tutorial. Prerequsite for this is being able to do a chest pull-up (overhand pull-up where you bring your chest to the bar) and a bar dip (starting
stiff-armed over the bar, lowering your chest to the bar, then pushing back up).
- Hang from the bar and swing your body forward. Right after the apex of your swing (as you're starting to swing back), do the chest pull-up. You'll feel the backwards swing pushing you to the back of the bar as you do the pull-up.
- Practice doing a pull-up and releasing your grip before you hit the top, then grabbing again. You should have enough explosive power to move up a bit vertically during the release. There's a grip switch for muscle-ups between the pull-up and dip parts, and this will help you learn it.
- Combine the prior two steps, swinging back into the pull-up and then doing the re-grip.
- Practice a reverse muscle-up (eccentric motion, I think), going to the top of the dip position, and lowering yourself through the motion, including the hand switch between the dip and pull-up part.
- Proceed to the full muscle-up. Don't be afraid to kip your legs while you're learning to gain momentum. It's practically necessary starting out.
One arm Push up
The two keys to this are balance and arm positioning. For balance, start with your legs spread to make the balance part easier. As regards arm positioning, you'll want to start with your hand further inwards and with your fingers point outwards to your side. The progression from a regular push-up to one-armed is basically one of progressively loading the arm with more of the bodyweight. I will assume you can do a regular pushup already.
- Side-to-side pushups: This is just a regular pushup, but shifting your chest over one hand during the down and up, then doing the other side. Start off with a smaller shift and continue working it until you can comfortably do pushups with the dominant hand at the center of your chest.
- Reduce the leverage of one-hand: Decide which hand will be the dominant one. The other one, move it to one side, or in front of you. As you descend, let the non-dominant hand slide out with a nearly straight elbow. You won't be able to as easily support your weight with it, which will force you to put more of your bodyweight on the dominant arm.
- Continue putting less weight on the non-dominant arm until it's largely just for balance. Now, you'll do the leg spreading trick for balance and just use the one arm.
As is always the case for push-ups, you can do progressions for any given step by having your arms start at a more elevated position. I personally skipped steps 1 and 2 when I started, because I was unaware of them, and started by doing one-armed pushups on a counter-top, then a chair, then a low platform, then the floor.
Your first step, as with most planche and lever moves, is to start with a tucked version. Grab hold of your bar, or rings, and bring your legs up and through your legs. Get used to hanging upside down for a time. Then, start extending your legs further, controlling your movement. Your first step will probably be a "skin the cat" where you let your legs go down past the horizontal into vertical. By doing that repeatedly in a slow and controlled manner, you will build up the core and shoulder strength to do the back lever.
One arm pull up