DA40 pilot reported they turned the wrong direction on a taxiway and entered a runway without clearance resulting in an aircraft on short final executing a go around.

Narrative

The event was a runway incursion at ZZZ runway XX and taxiway 1 at night due to lack of situational awareness; complacency; and task management; as well as unfamiliarity with the airfield. The taxi instructions given by ground were taxiway 2 then 1 to the XYL run up area. Due to lack of familiarity with the field and darkness; I initially taxied past the run up area after turning left onto taxiway 1; resulting in the need to do a 180 turn back to the run up area. I was told to advise once run up was complete. Prior to the run up check during the initial taxi; I noticed the oil pressure gauge was towards the lower end of the acceptable range; and this soon became my primary focus. During the run up; I was satisfied with all engine indications; however; a large portion of my focus remained on engine indications after the run up was complete. After the run up check; I was instructed by ground to cross XYL; hold short of XYR and switch to tower. However; since my focus was still on my engine instruments; I left the engine page up on the G1000 MFD without referencing the moving map ; and turned left onto taxiway 1; toward runway XX. This was incorrect; however during the time I mistakenly felt this was the correct direction; as taxiway 1 was the last taxiway given in the initial taxi instructions; and I incorrectly had in mind that I need to be on taxiway 1 before getting to XYL. Additionally; I was somewhat confused on my exact location after taxing past; and having to return to; the run up area. At this point; my focus was still mostly on my engine instruments; which caused me to miss the fact I crossed taxiway 3; and as I approached runway XX; I didn't take the time to verify that I was approaching the correct runway until it was too late. I was told I could cross runway XYL; and assumed that the first runway I was approaching would be XYL. I realized too late that I was about to enter the wrong runway; and crossed runway XX without clearance; causing an aircraft to go around. Furthermore; I did not hear the call the aircraft on approach made at the time; as that would have been another cue to watch for landing traffic. The only corrective action that could be taken was not coming to a stop on the active runway; as I was already past the hold short markings when I realized where I was. I was told to make a 180; cross runway XX; and cross XYL again. Only after the incursion happened did I pull up the moving map to reference the airport diagram for taxi. One of the largest contributing factors was unfamiliarity with the airfield; as was evident in missing the run up area. I believe complacency played a large role in this incident as well; as I did not feel I needed to take the time to double check my taxi routing; since the taxi instructions weren't very complex. Finally; task management was clearly a major factor; as I was focused on engine indications instead of where I was moving the aircraft. The biggest takeaway from this incident is to focus on the most critical task; and to separate tasks. There was no reason I couldn't have remained longer in the run up area looking at my engine indications until I was satisfied. There was also no reason to skip double checking taxi routing; especially at an unfamiliar field. Additionally; fatigue may have played some role; as it was towards the end of the day. There were multiple ways to avoid this incident. The first being asking for a progressive taxi from ground; as this would have eliminated any confusion about which direction to turn. The second being treating all runway crossings; no matter how routine; with complete focus and attention.