I asked a helpful lady at Sitges Tourism Office (+34 938 94 42 51). She immediately said that the best way from Barcelona Airport to Sitges is to take the 20 minute bus ride on Monbus from Terminal 1. It costs 7 euros per person. If you arrive at Terminal 2, take the shuttle to Terminal 1 and then take the Monbus.
She was not enthusiastic about taking the train from terminal 2 as you have to change trains and it might not be convenient.
Bus (MonBus) is the best option to go from Barcelona Airport to Sitges.
By Bus (MonBus): 25 minutes from Barcelona Airport to Sitges
Take the Coach Bus from Barcelona airport to Sitges. The journey from to Sitges takes less than 30 minutes and costs only 7 Euros.
Mon Bus runs every hour from Terminal 1 of Barcelona Airport. On weekends the frequency for the Barcelona Airport to Sitges bus is every 2 hours. You can see the schedule here.
By Taxi: 30 minutes from Barcelona Airport to Sitges
A Taxi from Barcelona Airport to Sitges can cost as much as 50 euros for the 30 minute ride. Consider taking the taxi to Sitges if you are traveling in a group of 4 and are not keen to wait for scheduled bus departures. There are private transfer companies who can drive your to Sitges in luxury, these are about 30 percent more expensive but they have options to take larger groups in vans.
Rent a Car: 30 minutes from Barcelona Airport to Sitges
The scenic coastal route to Sitges and traveling around the area at your convenience can be a good reason to rent a car from the Barcelona Airport
By Train: 55 minutes from Barcelona Airport to Sitges
Is it not convenient to take a train from Barcelona Airport to Sitges. There are no direct trains to Sitges, you need to change at El Prat de Llobregat. And train station at Barcelona Airport is in Terminal 2. If you land in Terminal 1 you need to first take a shuttle bus to T2 which is 4 km away.
So the journey to Sitges ends up being complicated : Barcelona Airport - Shuttle to Train Station in Terminal 2 - Train to El Prat de Llobregat - Change Train to Sitges.
In summary, MonBus is the best option to travel from Barcelona Airport to Sitges.
Note : If you are flying in to Reus or Girona airports do consider the extra cost of getting to Sitges against the cost saved by flying into Reus or Girona, vs Barcelona.