When departing KPNS (or any class B/C), you'll call Clearance Delivery before taxi and tell them which direction you want to depart, and they'll give you a squawk code and (maybe) what heading and altitude to fly immediately after takeoff. Then you call Ground to taxi as usual.
After takeoff, KPNS Tower will hand you off to Departure, who will likely give you a new heading and/or altitude once you're on radar. Ideally, you'll have climbed above the other Towers' airspace within a few miles and thus can stay with Departure the entire way out. If your climb performance sucks, they may turn you to avoid a handoff, or they might have a local agreement that lets them handle you anyway, e.g. if you're just going to clip a corner on the way up.
The key point is that as long as you're talking to ATC, they'll hand you off to whoever controls wherever you're headed next without you having to worry (much) about who that may be ahead of time. All those complicated lines are mostly just for folks trying to fly without talking to ATC.