I went to Barcelona over the Easter holiday with DH and DDs. We had a great time. I found tripadvisor really helpful for working out what places to see/do.
Although everyone takes on about the pickpocketing and bag snatching we were fine. Just use your normal, sensible, big city precautions as mentioned above.
Definitely book everything you can in advance over the internet to avoid standing in queues. This also means you won't waste time dithering over what to see. When you're there, if there's a new place you want to see, book it with your phone. I saw people outside museums doing this on the spot to beat the queues.
Park Güell (Gaudí spelled it with a k) is actually free but inside it there is a central area which requires tickets as does the house where Gaudí lived until he moved to camp at the Sagrada Familia building site. You can see the central area from outside. We had a picnic in the park and also had tickets for the house which is nice but v. plain compared to other Gaudí buildings
Nearby is Casa Vicens, the first house Gaudí transformed. It's small but incredible and pristine. We also toured La Pedera. Casa Battlo was covered in scaffolding but there are other amazing buildings on the same block. Palau Güell is just off las Ramblas and from there we walked down to the waterfront for great tapas at a café in a floating shopping mall.
We went round the Picasso museum and it's true - when he was young he painted properly and very well.
The metro/buses work well and a T-10 ticket can be shared. Confusingly the Barcelona transport system (renfe) and the national rail system (rodalies) both start with R. You can ride the metro directly from the airport into the centre so don't waste money on a taxi when you only need 1 ride/person on a T-10 ticket.
We also went to the Freixenet winery in Sant-Sadurní d'Anoia which is a short 30min train ride on the rodalies.