advice for someone who lifts heavy at the gym but wants to start calisthenics?

personally i lift heavy at the gym and try to progressively overload for hypertrophy but i realized i lack the basic body weight strength and can barely do 5-6 push ups easily. i want to start getting into calisthenics while still lifting at the gym. 

this might be a stupid thought but im not sure if calisthenics will come in the way of my lifting and muscle rest, hence stop my muscles from growing properly..if that makes any sense? 

also i don’t know where to start as a total beginner at calisthenics. my goal is to perfect a handstand or a headstand and a pull up but progress later on.

what’s the best thing i could do as someone who lifts at the gym and wants to start calisthenics? :)