The first beginner calisthenic chest exercise is the incline push-up. This variation is great for people who struggle with regular push-ups. You will need a chair, a ledge, a table, or anything to lean against.
The next exercise is the good ole fashioned push-up. It targets the middle and sternal part of the chest. It is important that you can do at least 10-15 push-ups before trying any other variation.