Anything less than a week for enjoying a country, regardless of size, would be a hurried and tiring affair.
So you really have to prioritize the places for your visits. I would suggest you cover these must-see
places during the first 3 days: Sentosa, Vivocity, Marina Bay Sands Resort, Clarke Quay,Science Centre, Chinatown, Litte India, East Coast Park,Singapore Flyer. And the rest with whatever time you are left with. Unless you have little children and they want to see the Zoo and Bird Park first.
To beat the hot and/rainy weather bring along a foldable umbrella, wet towels in plastic bag, small spray, etc when you venture out. The best days and times to travel so as to avoid unnecessarily huge crowds in public transport are weekdays between 9.30am - 5pm, and after 8pm. To avoid big crowds at eateries, go before noon, between 2 and 5pm and after 8pm. Long queues and inability to find seating other than these times may be a bit uncomfortable. And please be very familiar with offences and heavy fines regarding customs goods(including drugs,cigarettes,chewing gum), littering, smoking,drinking/eating on public transport/MRT stations, etc. :-))
Wish you a pleasant and enjoyable stay, and do some shopping which can be really worthwhile and affordable! :-))