B737 Captain reported a cracked L1 cockpit window during descent and a taxi clearance deviation once on the ground.

Narrative

During descent into ZZZ [airport]; the L1 windshield suddenly cracked and began arcing. I immediately turned off the L1 windshield heat switch; began to slow to 250 KIAS from the ATC assigned 300 KIAS and asked the FO to inform ATC. I then asked him to run the Window Damage procedure. We ran that procedure to completion and continued inbound to ZZZ. ATC (ZZZ Center) asked if we were declaring an emergency to which I declined. I felt since the airplane was flying normally and this was a crack in the outer pane of the windshield we did not need assistance. Upon check-in with approach; they had [given priority handling] us. The fire trucks were waiting for our arrival. After an uneventful landing we taxied in with the emergency vehicles following.Because of the event; they turned us west on [taxiway] 1 to taxi away from the normal flow of traffic. After we declined inspection by the fire trucks; we were given taxi instruction [taxiway] 2; 3; 4; and 5 to the gate. I misunderstood and taxied [taxiway] 2; 3 thinking we were to go to gate X and join the normal sequence of traffic into the ramp. As we arrived at the gate; ZZZ ground call and provided a phone number for the TRACON. They had a few question about whether there were injuries and the nature of the issue. I spoke to the Ops Manager and answered the questions. The ELB (Electronic Log Book) was entered; maintenance; manager and an Inflight Supervisor met us at the gate. I also made a PA upon arrival to the pax (passengers) to communicate why emergency vehicles had met us and followed us to the gate.