You can get an airport bus for 3,75 Euros. Goes to centre of Barcelona, Catalunya Sq I believe. 1 minute from Ramblas. Takes about half hour and gives you a good view of Barcelona. Very safe, good ride. You can pay on the bus. The stop is right outside the airport, which is not very big in itself.
Salsadancer is spot on, catch the bus, it's cheap and easy and drops you off at the top of the Ramblas, plenty of room to store your suitcase's on board and you save yourself about 30 euro.