At the earliest opportunity, it is a must that you get your SingPass. However, you can't until you are issued either a "National Registration Identity Card" (NRIC) or more likely a "Foreign Identification Number" (FIN). NRIC is only issued to Permanent Residents (PR) and Citizens so you will get issued a FIN with your first Employement Pass (EP), Work Permit (WP), Dependency Pass, Student Pass or Long Term Vistors Pass (LTVS).

With an identity card you no longer need to show your passport for transitions, with a SingPass you can use electronic entry systems and engage with hundreds of government and commercial websites with full security.