The short answer
For a first visit with three days, give Marina Bay, Chinatown/Singapore River and Sentosa one day each. Two to three main stops a day, with lunch, rest and room to adjust.
Day 1: Marina Bay
Merlion Park → Gardens by the Bay (Flower Dome/Cloud Forest) → Sands SkyPark → evening light show. Keep the first day light; you have just landed.
Day 2: Chinatown and the old city
Buddha Tooth Relic Temple → Chinatown street market → lunch at Maxwell Food Centre → Singapore River cruise → dinner at Clarke Quay. Comfortable shoes help.
Day 3: Sentosa
Cable car → Universal Studios or S.E.A. Aquarium → Siloso Beach. With children, swap Universal Studios for the aquarium and beach for a slower day.
Who it suits
First-time visitors with limited time who want the core. Add a fourth or fifth day for the Botanic Gardens, wildlife parks or neighbourhoods. With children or older parents, a private car and guide removes the transfers and queueing.