Securing accommodation in Zurich is not as simple as a first-come-first serve basis. The real estate agency and the landlord go through the applications and pick the most suitable tenant. So once you have your residence permit, which you'll need, try and arrive at appointments first, fill out an application for soon as, and come prepared with additional paperwork (like your employment contract, proof of solvency, and something known as a Auszug aus dem Betreibunsregister, which shows you have no oustanding debt. You can get this last document from the local constituency office, a place known as a Kreisburo.
For more useful info check out the "Renting Property in Zurich" page on Expat Arrivals.com