I bought some Citibank mutual funds(unit trust) & they opened an account for me. The credit card wasn't that difficult to qualify for, one only had to have a yearly income of $30k to qualify. When you are working for a MNC a credit cards is mandatory because traveling is required. The company will re-imburse all the travel expenses for the trips.
My active bank account was actually with POSB. Over the years I've had accounts with Standard Charter, HSBC, OCBC, POSB,.... After POSB was taken over by DBS I migrated to Citibank. My needs are simpler now. I only need a bank that can process the cheques I receive from the US.