How do I choose between building an emergency fund and building up a retirement fund (e.g. $1m by 55 y.o.)?

Depending on what age group you are at currently, but generally I'd build the emergency fund first, then retirement fund comes next.

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The more important question to ask is HOW do you build these funds. Make sure you have a solid plan for that.

Emergency fund first. Consider building retirement fund only when you are done with the "self protection" aspect e.g. when out of a job, down with an accident/illness.

I would recommend you have the emergency fund first before you consider retirement fund. By definition, emergency fund is something you'll need now, whereas retirement fund is something you'll need in the future.

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Your age will determine the size of your emergency fund, and how aggressive you should build the your retirement fund.

Build up both at the same time. Emergency fund using fully savings until reached at least 6 months of desired expenses. While doing so, as long as you are working, retirement fund is automatically building up via cpf contribution.

Consider transfering money from CPF OA to SA account if you have no near term need to buy houses. This will help superboost the SA account until it reached the max ceiling, any contribution from wages will then flow into OA account.

Use investment calculator online to calculate the savings and investment you need to reach 1 mil at 55yo.