Which is the correct sentence?

The first and third are equally acceptable. The second has an unnecessary comma.

The sentences are unacceptable in British English.

Why? It surprises me!

Barcelona is the Spanish city. It remains the Spanish city chosen for the Olympics, which is why you use present tense.

You would only use the past tense if it was no longer the case, as in,

“Barcelona was the Spanish city chosen for the Olympics until a last minute decision changed the venue to Benidorm.”

I take the point of the sentence to be past action. It was the city that was selected.

the first one is correct sentence.

You can simplify the sentence and retain the meaning by removing the relative pronoun which:

Barcelona was the Spanish city selected for the Olympic Games.

Ll was pointing out the English used by the English which is not the same as yours.