Via Taxi A taxi from the airport should take about 25 minutes and cost around 25 - 30 euros depending on traffic and luggage.
Via Train The RENFE train leaves the airport every half an hour and will take you to Estacio de Franca station, in about 33 mins and costs 2.60 Euros for a single ticket your hotel is a short 3 minute walk from the station.
Via Bus The Aerobus will also take you from the Airport to Catalunya station and costs 3.90 Euros. The journey time is around 30 minutes. From Catalunya you need to take the Green Line metro to Passeig de Gracia and then change for the Yellow line to Barceloneta. The hotel is 2 minutes walk from the metro.