Everything I mention below is for both men and women
Singapore is a westernized country with generally progressive attitudes, so you needn't worry a lot about clothing from a cultural perspective
If you're from Europe, Americas, East Asia, Australia, anything you wear normally back home in public will be perfectly acceptable in Singapore in public, including:
Very short shorts
The dress style is also very similar to North America. When you first land you likely won't even be able to tell how locals are dressed any different from you. So wear whatever you want!
The only exception is nudity, this includes being topless. In Singapore it's a crime to be nude or topless in public, or in private but can be seen from the public. This means, for example, that if you're topless at a private residence but people can see you from the outside, you've technically broken the law and can be fined up to $2,000 or even jailed for up to 3 months. In practice, no one ever gets into trouble for being nude or topless in private, but it's an absolute no in public (you can go topless on beaches if you're a guy, but not if you're a woman)
If you're visiting religious sites like temples and churches: you'll need to cover your shoulders, knees, and toes. So bring clothing and shoes accordingly
Of course, if you're attending events or going to private functions, dress code will be enforced. If you're going to fine dining, shows, casinos, etc. use common sense in terms of what you can and cannot wear. Again, the dress code for these events will usually be identical to what you're used to back home, or the organizers will tell you what the dress code is. So if you
The most important thing to think about is the climate. Singapore is very hot and humid
It's almost always above 30C during the day:
And humidity index average 82% throughout the year
Despite the heat and humidity, it's not a problem at all if you're planning to spend most of your time indoors. AC is everywhere (including all forms of public transportation) and usually set to 20-22C. So as long as you're in doors you'll be very comfortable
But if you're planning to do a lot of exploring and walking around outside, dress very light, and wear breathable materials, or you'll be drenched in 30 minutes. Wear comfortable shoes because Singapore is a pedestrian-oriented city and you will be doing lots of walking.
Finally, pack a light rain jacket and/or an umbrella, because it rains regularly in Singapore