Corporate jet Captain reported confusion about their position during taxi after landing at LGB led to a runway incursion.

Narrative

On day 0; after landing on runway 30 at long beach airport (LGB); we were instructed to exit via taxiway A due to a brief loss of situational awareness and confusion with signage; we mistakenly turned onto runway 26R which was active at the time. As soon as we realized the error; we exited the runway immediately. The tower later advised that an inbound aircraft had to go around due to our incursion.After clearing the runway I taxiway D; my copilot and I experienced a brief delay in contacting ground control. The confusion of previous deviation and our focus on safely clearing the area caused a few moments of hesitation before we reestablish communication. Once contact was made; we received taxi clearance and proceeded uneventfully to the ramp.Since the event; I reviewed the airport diagram thoroughly and committed to requesting progressive taxi instructions when operating in unfamiliar airports. We have also emphasized strict cockpit procedures during taxi and ground operations.This report is submitted in the interest of aviation safety and accountability.