The tourist office has a 2-hour walking tour of the Barri Gotic that I enjoyed. It was 16 euros last year. I believe it ran only once a day, and perhaps not every day of the week. There are also "free" walking tours done by one or more private companies. The ones I saw seemed to be larger groups. It is expected that you tip the guide if he or she is competent.
If you wish to see the Palau de la Musica Catalana, that requires a guided tour conducted by a staff member. English tours are frequent but you can't necessarily walk up to the ticket counter and find space on the next tour, especially as a group of 5.
Otherwise, you can go it alone if you wish. Many sights have English-language audioguides available (often covered by the price of admission).
The issue in Barcelona is that many of the sights can suffer from very long admission lines, so you need to book entry and/or buy tickets ahead of time. Not necessarily before you leave home, but a day or two in advance of the day you want to visit. Not doing so risks spending an hour or more in line, which would be a shame because there is a great deal to see and do in the city. And Barcelona can be hot.
These are places I wouldn't want to walk up to without a ticket:
Camp Nou (soccer stadium)--and those entries may well sell out quite early; I do not know
Picasso Museum (tends to be a mob scene; skip if you are only marginally interested)
La Sagrada Familia (and a separate timed ticket is required if you want to ascend a tower)
Casa Battlo (tends to be slightly more mobbed than Casa Mila)
Casa Mila/La Pedrera (only marginally less busy than Casa Batllo)
Parc Guell (outdoors; you don't want to visit mid-day if the weather is hot)
In my experience you don't need to make advance bookings for the other art museums or for the blessedly-uncrowded-as-of-last-year Sant Pau modernista site (though I think there's only one English tour per day at Sant Pau).
If you want to go to Montserrat, that's easily managed on your own via public transportation.
I've had no problem with pickpockets in Barcelona, but the city seems to have more than its share of them, so it's a place you definitely don't want to be carrying excess cash, credit cards, ATM cards or other valuables in pockets, purses or bags.