From the bodyweight perspective: pushups and dips variations are what you want. Dips require some equipment (dip bars or chairs etc) so I’ll focus on pushups. Remember good pushup form should also reasonably be a decent ab workout and should have lat engagement as well. You’ll also develop your shoulders pretty evenly.

For the basic principle; warm up via easier pushup variations and then do your work sets using the most difficult pushup variation you can. If you want, you can finish up by dropping down a level or so and then working the muscles to exhaustion as well (although I don’t enjoy this).

Warm up:

• Kneeling Pushups: 1 set of 15-20 reps
• Rest 90s - 2mins
• Pushups: 1 set of 10-15 reps

Work set(s):

• Close Pushups (hands together): 3 sets of 8-20 reps depending on ability
• rest between 90s and 3mins between each set

Bonus sets:

• Pushups: 2 sets to failure, remember to stay safe; don’t commit to a rep if you can’t complete it.
• Rest between 90s and 2mins between each set

Remember if you’re building your chest and triceps you should also balance this out in the grand scheme of things. I developed a shoulder injury caused by having an imbalance between my chest and back and shoulders because I neglected pull-ups; balance out this workout with a pull-up workout (or do it in the same workout).