Top three? Not sure I could come up with just three
If its important to you, bring it with you (assuming shipping is not on your nickel) Favorite books, photo albums, artwork.
I'd pack a carton or suitcase with favorite items from the drugstore: vitamins, over the counter drugs (you might want to see the other thread on this) any convenience item that will make your transition easier. You'll be surprised, there are a lot of things that are available here, and a lot that you may miss, so treat yourself and get what you need so you can find a suitable substitution on your own time, not as soon as you land.
Shoes for the whole family (running/tennis shoes are easy to find, real shoes can be tough -- either very cheap or very expensive). Likewise for clothes -- if you have a favorite pair of shorts -- buy them in every color.
If there is something you've always wanted but didn't want to splurge on beforehand, do it now and stick it in your shipment. Or buy it when you get here (like a second KitchenAid Mixer, a wii for the kids, etc...) Treat yourselves, this is a big move and some aspects maybe hard, so balance it with some good if you can.
Fill up a carton of DVDs and books.
Recognize that for all it's westernized outward appearances, Singapore is a strange and different place and that most people face a sizable bit of culture shock when the honeymoon phase wears off. Some are cavalier and deny it, but it's there. This isn't a sign of failure or weakness, or a shortcoming of Singapore itself-- it happens when people move. Kids regress, spouses get cranky.
If at all possible, have the working spouse take a few days off when you land to help you both get your feet on the ground. Nice for the both of you to take ownership of the situation, so one spouse doesn't feel dragged into the situation or abandoned. I have friends that work in relocation companies who claim this happens a lot.
Don't rely on just one agent. They can be woefully uninformed. Do a lot of research over the internet and ask a lot of questions. Look in the Straits Times and ask to see specific properties if they appeal to you.
A smart question to ask, good luck with your move.