The most comfortable way to travel from Barcelona airport to Tarragona is by pre-booking a Barcelona bus transfer or a private taxi transfer.
From BCN airport there is a bus service to Tarragona. The fare is usd 18/eur 15, and the journey takes 1 hour and 5 minutes.
You have more flexibility when booking a taxi as it will take you directly to your accommodation. Especially when you share a taxi, this can save time and money.
A minivan for 6 people is available from € 26 per person including your luggage.