Singapore is rather small in size and the public transportation system is well developed and reaches most parts of the country. For example, the subway system (MRT) has a line which runs from the Changi International Airport to the rest of the city. Therefore, it is quite easy to move about even if you are carrying your luggage.
The weather is generally hot and humid for the large part of the year. Rarely does the temperature falls below the mid 20 degrees in the day time. So, you do not need any warm clothing. Something light is ufficient. On the other hand, an umbrella may be handy at times, but you can probably buy it in Singapore if you have to (except you may not be close to any store when you need it most).
Singapore is an international city, with free movement of goods and people. So, it has practically everything you can find in all major cities in the world. As there are shopping centres and shops everywhere selling practically all the daily necessities, things that have been left at home can most likely be bought in Singapore although you may not be able to buy the brand of your choice.
Similarly, pharmacies can be found in many places, but many types of medicine can only be bought with a doctor's prescription. Also, prescriptions issued by doctors outside Singapore may not be entertained. So, visitors should bring along sufficient supplies of medicine for their own use. If they are short of medicine for whatever reason, they may have to visit a local doctor for help.