I joined as a post-doc fellow at one of the research institutes in Singapore as soon as I got my PhD. As a fresh graduate, I got S$4300 per month (plus 13th month bonus, and only paid <10% tax). I learned it was a fair pay - a friend of mine in NUS made only S$3500 as fresh graduate and others made more than me.
As far as I know, not many institutes nowadays would pay housing allowance, unless you are qualified to be considered as foreigner (staying out of Asia region for more than 5 years). You need to check with your employer whether you will be employed as local or foreigner term.
I am now working in Sydney. Got about AUD$4600 per month (without the 13th month bonus, plus have to pay >20% tax!!!) after post-doctoring experience in Singapore.
The SHIFT scheme is, as what I heard, not a good scheme. You might be better off to hunt for a room or house in the market.
Hope this help.