Our party of 4 adults and 5 children stayed two nights at Marta's place.
It is 20 minutes by the 46 bus direct from the airport to just outside the apartment, very easy. Marta met us there, she is SO lovely, very helpful.
From outside the apartment you can take a bus into the heart of the city in 20 minutes, or it is 10 minutes walk to Pl Espagnol where the Metro can take you anywhere.
The apartment is really nice, 4 double bedrooms, 2 bathrooms, a nice living/dining area, and a kitchen with everything you'd need for a few days.
We had no problems at all, Marta helped us with anything we needed. We walked 20+ miles around the city, and used buses and the Metro (buy the T10 ticket for travel, great value).
It's a lovely apartment, Marta is a fabulous host, Barcelona is a beautiful city.