Calisthenics, at least when you get past the basics, is almost equally a skill as well as a strength requirement. Here's what I've found helpful for myself. I'm not advanced at all in calisthenics as I spend most of my time climbing. However, I have a front lever and a dragon flag down, so I don't consider myself a total slouch.
ALWAYS use perfect form. Drop your ego with numbers. If you are sure you can do 10 pull-ups right now, but your shoulders are internally rotating and your body is swinging, you can't do 10 pull-ups. If you're on your last set of an exercise and are struggling to hit the number of reps you wanted, STOP. You are unable to do that many reps and that's perfectly fine. You need to train your body to move properly and activate the right muscles just as much as you need t o make it stronger. And if you are cheating form at the basic level, it will just take you longer to move to the more advanced level of that movement pattern. (This is all speaking from experience)
For upper body, get strong in pull-ups, push-ups, dips, and inverted rows. You need a certain level of strength to even begin attempting more advanced moves like muscle-ups and levers. Once you are strong enough to begin practicing a regressed version of an advanced exercise, like a tucked front lever, work that into your training. Again, you need to build skill and strength at the same time. There are articles all over T-nation and the internet in general that will tell you how you can progress a movement pattern to make it harder over time. Find the ones that work for you.
For legs, use weights. You'll simply get stronger more quickly (also speaking from experience after months of wasted time). Squats and deadlifts are enough. Again, use perfect form and check your ego on the weight you use. If you look at a lot of the guys who only do calisthenics you'll notice they're usually shirtless and wearing sweatpants. That's because they don't want you to see their legs. Their legs are weak. That being said, one-legged squats are great and require skill and strength. Add some practice of those to your regular strength work.
I found this super helpful as a core training progression. This will prepare you for dragon flags. Like I've said already, form must be perfect or you're not getting anything out of it.