hi there,
Taking the SMART is the best way to get around Singapore as it's economical and fast and you won't get stuck in traffic jams.
There is a train station in Changi Airport itself ( Terminal 2 ) so from there you can go to most
places plus you get lovely views of the city so it's great.
Equally efficient is
Singapore bus system . Buy a contactless "EZ" card to get around the train and buses. It's available at all MRT stations.
Hope this helps
Vacationbuddy