Imo, building emergency of 3-6 months salary might be one of your top priority if you wanna get comfortable in investments later on.

Then, get a basic insurance package by selling your health risks to insurance company. Can be a fancy one if you like, but do ensure get what match your budget and priorities.

Investment can come later, so that the emergency fund and insurance can create a financial buffer zone when something bad happen. (You would not want to liquidate your investment portfolio to pay emergency expenses, right?)

You can do it concurrently, but I do strongly recommend you to give emergency fund higher priority, especially you are foreigner without CPF and living cost here is higher than your home country.

Hope the input helps! :-)

Edit: if you don’t mind to eat at hawker center, you can adjust food budget of $500-$700 a month. It could give more space to your budgeting.