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Virtually everything you need is readily available in Singapore.
The only things you need to bring are items of emotional value, which are thus irreplaceable - and of course a few clothes for the first days (hot summer items - it is never cold here!).

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I forgot to mention: Money!
Singapore is one of the costliest places on earth and especially in the initial weeks and months you will face irregular expenses (deposits, furnishings, etc.) before your first salary is paid, so bring as much as you can - I would recommend a minimum of S$2000-3000 per person.

Accommodation:
If your are staying in fully furnished house, then you have to just buy some vessels for cooking, bed spread and pillows (if not available in the house). You can buy everything in Singapore instead, carrying them from your hometown.
2 bed room cost - S$1900  to S$2100
1 bed room cost - S$900 onwards (shared space)
Cost will be higher, if you are staying in a condominium
Food:
For initial days, you can have food in hawker centres or any near by restaurants
At the max you might require S$30 per day ( you will end up paying less in reality)
Clothes:
Bring some formal and casual clothes for initial days/months, as you will find a lotssss and lots to purchase in Singapore. You will the meaning for spoilt by choice.
Medicine:
Bring all your regular medicines with doctors prescription, medicines are pretty expensive.

Thank you so much everyone for your feedback.
The school is paying for baggage and I was wondering whether I could save a bit bringing in  some of the required stuff.

Well, of course, in that case bring as much as you can of the more expensive items and buy the cheaper ones new.