Regardless of what gym owners and mainstream bodybuilding media say, you can reach your upper body genetic potential by doing only bodyweight exercises, which can be modified in many ways to ensure lifelong progression. The extremely well developed upper bodies of gymnasts are a testament to that.
CHEST and TRICEPS
The dip and the push-up can be made harder and harder through variations. A classic approach would be to add weight, but you can certainly get decent results without additional load.
You can start with regular dips and push-ups, build up to high numbers and then transition to performing the same exercises on gymnastic rings. The numbers will naturally drop because the movements become much harder when done in unstable environment.
Thenceforth, you can move on to harder variations such as muscle-ups, planche…etc. The progression is literally endless. The downside is that if you are tall, you may feel frustrated if your goal is to reach extreme gymnastic skills. However, dips and push-ups are certainly still a good chest builder even for lengthy guys.
Note: A general progression for dips would be to first reach 3 sets of 20 quality bodyweight reps before adding weight.
BACK and BICEPS
Pull-ups, chin-ups and horizontal rows will build your biceps and back. If you add other exercises such as hyperextensions, your lower back will be quite strong too. Similar to dips and push-ups you can either progress to harder variations, such as the front lever, or simply add weight. To be quite fair by adding weight you are combining weight training and calisthenics, but who cares?
Note: Before adding weight to your pull-ups and horizontal rows, you should be able to do 3 sets of 15 quality reps with just your bodyweight.
Highly recommended article: How To Do Barbell Rows With Proper Form For Maximum Gains
What about barbells and dumbbells?
I would be wrong, if I tell you that barbells and dumbbells cannot build a super strong and thick upper body. It has been happening for centuries. The bench press, the row and the overhead press will make you a strong muscle ninja. However, I would say that the muscle mass offered by these movements can be achieved with bodyweight drills also, and if you prefer to train outside of a gym, calisthenics are the way to go. You are not missing on anything, especially if you are natural.
Are all popular calisthenics legends natural?
Some are but not all. Many popular calisthenics masters have obvious cases of gynecomastia. One of the them is Hannibal For King. You do not get gynecomastia at 35+ years of age when you are 5-8% body fat just like that.
Another more than obvious example would be Kali Muscle who is 240 lbs. shredded and still does bodyweight exercises, although he performs them for a show rather than training.
Note: The fact that someone has incredible bodyweight skills does not make that person natural. You can be abusing a lot of anabolic steroids and still by a calisthenics follower. Nonetheless, there are more natural people in the bodyweight community than the bodybuilding sector.
What about legs?
You can build decent legs with sprints, bodyweight squat, pistols, Bulgarian split squats, skipping rope…etc. However, barbell training certainly owns bodyweight drills when it comes to development of brutal leg strength and hip power. Who has stronger legs? The person who can squat two times his bodyweight or the guy doing 15 pistols. They are both strong but the squatter has higher absolute strength. Of course, one could argue that bodyweight exercises come with the added bonus of improved flexibility and require the trainee to have low body fat levels.
If you have access to a gym, dedicating time to developing your squat and deadlift will always be beneficial for your training career. In the end, combining the best of both worlds has always been the ultimate solution. If you have good judgment built on experience, you should just do what feels right to you.