Don’t take a tuk tuk! Aside from it being expensive, they are limited to local roads so it takes longer and the pollution is worse. From the airport always take the bus.
Leaving the Airport
There is an ac bus which leaves from outside the airport, turn left and cross the drop off lane and walk 100m to a fenced parking area. The buses leave every 30 mins sometimes more often and cost about 120LKR. Ignore the taxi and tuk tuk drivers in the area. They will tell you that there are no buses, only taxis.
Arriving in Colombo
The bus arrives at Pettah Central Bus Stand and takes between 30 mins and 1 hour depending on traffic. In Sri Lanka you pay the conductor who moves around the bus issuing tickets after the journey starts.
There is space to store luggage and it is free although some locals may try and charge you.