Pilot reported an unfamiliarity with the airport; misinterpreting ATC instructions; and confusing taxiway signage contributed to a taxiway incursion.

Narrative

Incident occurred during taxi from FBO to runway XXL at ZZZ. After crossing runway YY at [Taxiway] 1; I inadvertently turned onto taxiway 2 rather than continuing on [Taxiway] 1 due to my unfamiliarity with the airport and slightly confusing signage. This caused the ground controller to issue new instructions including a hold short instruction for [Runway] XXL which I later listened to via a liveATC.net recording. I misunderstood the instruction as a cross runway XXL and hold short [Runway] XXR due to my lack of situational awareness and rushing due to my previous taxi mistake. Upon reaching [Runway] XXR at [Taxiway] 3; I followed the instruction to switch to tower frequency; cleared runway visually noting an aircraft on what appeared to be a 3 mile final. On my initial call to tower I informed the controller of my current location and status of crossing [Runway] XXR. I heard the tower instruct the traffic on final to go around due to my incursion. By this time; I was across [Runway] XXR and taxiing to the hold short line of [Runway] XXL.The incident occurred due to my misunderstanding of the ground controller's instructions; rushing due to the earlier taxi mistake and not properly verifying the instructions when I stopped and noted traffic on final. In retrospect; regardless of whether I thought I had a crossing clearance; I should have held short of [Runway] XXR anyway and verified crossing instructions upon noting the traffic on final which would have caught my mistake. Additionally; regardless of confusing signage; in a world of GPS located airport diagrams; there is no excuse to get turned around at a taxiway intersection. Even if that occurs; slowing down and making sure all instructions would have prevented rushing which was the root cause for this mistake. Lesson here is to slow down; be thorough; and when in doubt; ask for clarification.