Push-ups are the classic bodyweight movement that trains the horizontal pushing pattern. The taller the incline the easier the exercise. Start with the height where you feel most comfortable!
The vertical push traditionally trains the shoulders from an overhead position. It is the prerequisite to learning the handstand. But many people will also throw dips into the vertical push category as it focuses on the shoulders and triceps.
If you’re looking to build some strength in your upper back, the horizontal row is one of the best ways to do it. This exercise does require some equipment, but it is cheap and simple to get.