I live in the building next door to the Hyatt and here are my recommendations:
- Small bag - MRT from airport to Orchard station and walk
- Small or large bag - To get to the airport, I would recommend the #36 bus from the bus stop in front of the Tang (Marriott) dept store on Orchard Rd. No change of bus is required and takes the same amount of time as the MRT. The bus does a small loop when coming from the airport (extra 8 mins I'd say), so I generally take the MRT.

Taxi - the lowest I pay during off-hours is $16-17 to the airport and $19-20 from the airport. Since the recent fare increases, there is a very small window when you don't get hit with the surcharges, so expect to pay around $20-23 on the way to the airport and $24-26 from the airport. Add $2 on Fri-Sun evenings when coming from the airport.