OK I sense TS may not be very sure what he needs or wants but he is just hearing a bunch of stuff here and there.
Why buy insurance? For financial protection against something bad. In particular you want to insure yourself against somewhat likely, big impact events.
First, you are probably enrolled in
Medishield, which is
hospitalisation and surgery insurance, and also covers some procedures for outpatient treatment such as chemo. But there are limits to how much it pays out depending on the procedures, which hospital ward you stay in, and even how much income you earn (means testing). Right now the government is rolling out
Medishield Life which will eventually be universal and builds on Medishield. Many people (apparently 60% as reported in the news) buy Integrated Shield plans that build on Medishield and pay out more, particularly if they want to stay in A-class wards or private hospitals.
If you have such a policy and touch wood you have to stay in hospital and incur a large bill, ideally most of that bill will be paid for by the policy and the rest can be paid through your Medisave or if all else fails cash. This is the most important because (1) out of all the high impact bad health events, it is the most likely to happen; and (2) it could do you severe financial damage. You should find out what coverage you have - Medishield or an integrated shield plan - and whether it does enough of what you want.
The second most important IMO is
life insurance, meaning insurance that pays out upon death, terminal illness or permanent incapacity (or total and permanent disability). If you did not opt out, you should be under the
Dependants' Protection Scheme which gives a sum assured of $46,000 up to age 60, premiums paid from CPF. But if you are a or the breadwinner and you have dependants, and if you pass on early, this is probably not an adequate sum. How much is considered adequate depends on the person, but usually people aim to replace at least many years' income or expenses.
To get adequate life insurance people can buy two kinds of policies: term and whole life. In a term policy, you only pay for the insurance coverage and the coverage lasts only when you pay for it (kind of like car insurance or house insurance). You do not get any money back. A whole life policy technically combines insurance and savings/investment - you pay a lot more in premiums, but the insurance company invests your premiums and your policy has cash value. People on limited budgets and/or high insurance needs should look at term policies such as the
SAF Group Term Life Insurance by Aviva.
Third in importance is a toss-up between two types of risks. One is
critical illness, which is a standardized list of 30 serious major illnesses. Although hospitalisation, surgery and some kinds of treatments will be covered by H&S insurance, coverage for CI can help to replace lost income or to pay for excluded treatments and drugs.
The other is
disability. There is a semi-compulsory policy for age 40 and up called Eldershield which covers severe disability i.e. need for long-term care. But there are also more wide-ranging policies that cover work disability meaning the inability to carry on one's original occupation or something equivalent. These policies generally pay out some amount per month, for some years or until a given age, and are meant to cover ongoing expenses for care or replace income.
Then there are the less important kinds, because less impact or less likelihood, but nonetheless get marketed a lot. Personal accident insurance - only pays out for accidents. Early critical illness, or other kinds of major illnesses. Something like an endowment plan
does offer insurance coverage, usually life and TPD, but its primary purpose is savings/investment, such as a parent who wants to save for his child's university fees over 15 years.
TS should verify what coverage you now have, particularly Medishield and DPS, and then engage an insurance agent or financial advisor for the rest.