You want to build a big chest. How do you do it?
Muscle grows in response to gradually increased loading with progressive resistance. To build a bigger chest you need to increase the loads you move with your torso muscles.
Your chest circumference includes your upper back and pectoral muscles. The main upper back muscle is the latissimus dorsi, the large muscle that gives you a V shape. The lats are much larger than the pectorals, with a greater growth potential. Therefore if you want a big chest, you should place a priority on building up your upper back.
Some good exercises for building up the upper back are
Chin ups are better than pull ups with a pronated grip because they put the biceps in their strongest position which means you can load the upper back with higher resistance and you simultaneously get the best bicep exercise.
Parallel grip pull ups and front lever variations are also very good upper back movements for building a big chest. Parallel grip pull ups are a variation of chin ups, and front levers are a lever progression of 90º pull ups.
If you can't yet manage 90º pull ups you can scale down to inverted rowing.
You really only need chin ups and rowing or 90º pull ups to adequately train all the muscles of the upper back, but if you want to also master front lever you can alternate front lever training with 90º pull ups training.
Generally when training for mass, simpler is better. Focus on getting very strong in chin ups and 90º pull ups.
To build a big chest you should use the best chest exercises.
Contrary to popular belief, it is not necessary nor desirable to use many different chest exercises from different angles. The pectorals are best trained with parallel bar dips and horizontal pushing movements like push ups (floor or rings), or barbell flat bench press with shoulder width grip.
You only need 1-2 good exercises. The most important thing is progressive resistance. Focus on getting very strong in just one or two of these movements.
To build a big chest, you need to Get Strong!
Bodyweight chin ups and dips won't build a big chest, no matter how many reps or sets you do.
For the upper back, you need to think in terms of gradually building up the ability to do 6-10 chin ups with 100-150 pounds of added external load (barbell plates), or with one arm.
For the pectorals, think in terms of doing 6-10 dips with double bodyweight (your body plus external load equal to your bodyweight), or 6-10 push ups or bench presses with 250-300 pounds (for push ups that would be body mass plus added band resistance).
The body strives to keep everything in proportion. If your legs are weak and small, it will only permit limited increase in chest size.
In addition, hard leg training increases your respiratory demands, which can expand your rib cage for a bigger chest.
If you want to build a big chest, you should also work on building big, strong legs.
Now we are talking building up the ability to squat 5-10 repetitions with 250-300 pounds.
To build a big chest, your training program should include only 10-12 total exercises for the whole body, most of them multi-joint, including:
You should perform these exercises with limited sets, with a frequency that allows weekly strength gains, over and over until you get very strong. Your sets should be limited and your frequency adjusted so that you gain strength every week.