If you are staying/working in Singapore with the relevant pass, you should be able to purchase health insurance in Singapore.
You should be able to find many options on getting hospitalization coverage. However, for cover on outpatient GP and Specialist, the choices are limited.
Plans that cover the full suite (outpatient + inpatient) are usually international plan that may cost thousands to cover a family.
There is no medical subsidies for non-Singaporean, so there is no incentive to be warded in a government facility. When you are sourcing around, look out for Plan that allows you to be warded in private hospitals. Other things to look out for are:
- Waiver of deposit at admission
- Worldwide cover
- Bed entitlement
- Sub-limit or lump-sum cover
- Coverage on pre-existing condition
- General exclusion and etc.
Btw, the cost of a single bed ward at Gleneagles hospital is $460 per day before taxes.
You can get a feel of the hospitalization cost in Singapore at
http://www.moh.gov.sg/mohcorp/billsize.aspx?id=302