What are some insurance plans I should buy for myself at age 56 and for my child who's 20 years old?

1) Term insurance covering death, TPD and CI as your child could still be your dependent till he/she starts working
2) Your child should have a hosp plan

Bear in the mind the premium costs as I see the agent's recommendations are very expensive in total. Good for his commissions though haha

To be honest with you.

There is not much runway for you to buy CI protection due to the premiums required to fund it. It likely should be in the range of 7%-10% of premiums paid. Hence, if you really want some coverage, the best is to self-insure in this case. However, there is a possibility to get CI coverage for up to 5 years just for you to prepare a bit of emergency funds for self-insurance for CI. (or you may not even be able to buy CI protection).

Your current runway is to get the elder type of insurance for yourself, depending on your finances.

For your child at 20 years old, it depends on whether you want consistent returns of 3.5% to 4% on a whole life policy (which also has a higher premium), or buy term and invest the rest, which you can easily beat if you invest more aggressively for your child. But I would urge you to get private insurance (be it a term or whole life) first since the premium compared to Mindef Aviva is very similar, and having a private insurance locks in the premium as compared to some possible change to premiums.

Also, the guaranteed insurability option allows your child to upgrade with no underwriting required should there be insurability issues that developed later.

Mindef Aviva Term death should be a top-up requirement compare to a private when your child reached 27 years old and above.

The list of insurance to consider is the same as you by right for a single,

Hospitalisation protection first covers medical bills

CI protection - covers 5 years annual income for your child

Death (after he starts working and maybe giving you some income)

Accident/disability income (depends on what kind of job etc).