even as a tourist, you can open a saving account with DBS (
www.dbs.com.sg). if you got all the right paperwork, they will open an account for you immediately and with an ATM card. with an account number and a SWIFT code, you should be able to electronic transfer funds from US to singapore. so open an account asap when you are in singapore.
cash is king, so bring as many as you feel comfortable with. with cash, you will get a better exchange rate with the local money changer dotted everywhere in singapore. tip: shop around a few money changer as some rates are better then others. you can even haggle if you are exchanging a large amount.
moving large amount of money in or out of singapore is best done with a money broker such as
www.hifx.com (i dont work for them or even use their services!) instead of the local banks. the rates are better and the fees/commision are less (or none).