If you are visiting Barcelona on a budget the tour bus can be expensive and if you don't want to follow the crowds you might be better off buying a T-10 card and explore the underground and bus system. You have 1:15 time to commute between buses etc. each time you mark the card.

Another option, mostly a trap for clueless tourists who have not much time nor will to explore around, is to take the Barcelona Bus Turistic. It's 19 Euros for one day or 23 Euros for 2 days. Catch the bus from the Plaça de Catalunya and try to get a seat on the open top deck (if you are able to afford the long queue under the sun). The bus has three routes that are interchangeable. You can hop on and off the bus as many times as you like. There are 6 places where you can change from one colour route to another or just get off at one of the 44 main tourist sites. To complete all three routes will take about 6 hours so day one is pretty full.

The RED Route includes amongst its highlights Gaudi's La Pedrera (The Casa Mila) and his Sagrada Familia. For football lovers FC Barcelona Stadium and for art lovers the Museum d'Art Contemporani de Barcelona (MACBA).

The BLUE Route takes you round some of the cities popular shopping areas, past the 1992 Olympic Stadium and Olympic Village, check out some of Miro's sculptures, the World Trade Centre and finally the Barri Gotic.

The GREEN (Forum) Route concentrates on the area around Poblenou.

And now on the souvenirs:

First, do not make a fool of yourself: do not buy a Mexican hat. Those are good for the business of the souvenir shops for tourists,
but not for the visitor. This is not Mexico, that hat only makes you look like a fool. If you are afraid of the sun, which you have reason to avoid if you are a pale rose individual, buy yourself a good hat or cap, and cover those shoulders too: the ones ith shrimp red skin the next morning will understand that advice, even if too late.

Never buy a Spanish flag with the bull and wave it around. The souvenir shops as above will be very happy with you as a customer.
But that piece of cloth will only make you look like a clueless foreigner here in Catalonia.

Side note: other than match days, only tourists or children wear football t-shirts of Barca Football Club on the street.

Locals will spot you as a tourist as well from miles away, but at least will not categorize you into the bovine tourist set, and will be more likely to answer your questions and help you.

Have a nice stay.