General aviation pilot reported a runway incursion during taxi from the FBO and crossing onto a runway; causing another aircraft to perform a go around to avoid the conflict.

Narrative

I was parked on the ramp. Called Republic Ground with the current ATIS and stated I was ready to taxi for VFR departure to the east. The Controller asked me a question and I was unclear what she asked me so I stated that I did not understand what she was asking me. Then she restated the question asking me if I was closer to Taxi G4 or G3. I looked up and saw G4 just a few hundred feet from me so I stated I was closer to G4.I was told to Taxi to 19 via G4. Normally I pull up the airport map and draw a path from my present location with the path i am to taxi to the runway but this time I did not do that. I did not pull up the airport map. I thought I would taxi down G4 that was in front of me to Runway 19. I should have found the airport map and drawn out exactly what my taxi path was to be to ensure I clearly understood what I was being asked to do. Unfortunately I did not do this.I thought I understood the directions and proceeded to taxi from the FBO ramp toward G4 and continued on G4. I must have had cognitive dissonance at the moment of arriving at G4 and Runway 19 because the runway marking did not register in my head since I though I needed to taxi to 19 -- It seems stupid now but somehow I had in my head that the duration of my taxi would be some distance.I somehow missed the fact that I was literally parked on the ramp just a few seconds taxi from the hold short line at Runway 19 and G4. As I approached G4 I said out loud to myself 'Taxi 19 via G4' and proceeded on G4. In a couple of seconds I realized I was in the middle of the runway so I hit the brakes and stopped. There was a Aircraft Y that was on final approximately 500' or so down the runway with 50' or so of altitude. The pilot of the Aircraft Y began to climb.I turned the aircraft around and exited Runway 19 via G4. I stopped on the ramp area out of the way of any taxiing traffic and stopped to think about what just happened. I pulled up the airport map and then realized that the FBO's ramp essentially ends at the hold short line of Runway 19 at the taxi intersection G4. The function of G4 is essentially to take traffic on and off Runway 19 directly into the FBO ramp or to maneuver for Taxi G.From now on I will always refer to the airport map and draw out my taxi rout to ensure I completely understand where I am supposed to operate on the ground. I am so upset with myself for deviating from my usual operating procedures for taxiing at controlled airports. The one time I do not take the time to pull up the airport map and clearly go through my position and where I am to taxi and stop and where are the hot spots and potential hazards etc. I ended up doing something stupid. If I'm honest; My brain must have been distracted because ordinarily I would NEVER have crossed the Hold Short line on the runway. I do not know where the focus of my brain was but at that moment it certainly was not focused on a safe taxi.