Sort this out and the rest is easy.
Take the train in from the airport
Skip the taxi queue. The train’s comfortable and it drops you at Passeig de Gràcia, dead centre. You walk out of the station into the middle of everything.
Line R2 Nord from Aeroport station, attached to Terminal 2. From Terminal 1 take the free shuttle bus, about ten minutes. Half an hour to Passeig de Gràcia.
Open in Maps
Buy a T-casual before you do anything else
Ten journeys on one card, much cheaper than singles. Works on the metro, the buses, the tram and the local Rodalies trains. Two of you can’t share one, so buy one each.
Any metro machine sells them. Trips further out, Sitges especially, need extra zones; enter the destination and the machine works it out. Fares change, so treat any price you read online as a guess.