What scriptures did the Bereans search?

The Answer is: The Hebrew Old Testament.

Remember Acts 17:1-3 explains what Paul did and taught when he first entered into a new city: 

“Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews:  And Paul, as his manner was, went in unto them, and three Sabbath days reasoned with them out of the scriptures,  Opening and alleging, that Christ must needs have suffered, and risen again from the dead; and that this Jesus, whom I preach unto you, is Christ.”

The “scriptures” here is the Old Testament.  I Corinthians 2:2 Paul explains his initial preaching:

“For I determined not to know any thing among you, save Jesus Christ, and Him crucified.”

Paul would first teach that Jesus is the Christ, then would explain the crucifixion.

Even the events of death, burial and resurrection, were historically predicted in the Old Testament as I Corinthians 15:3,4 say:

“For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures;  And that he was buried, and that he rose again the third day according to the scriptures.”

So Paul used the Old Testament scriptures to teach that Jesus is the Christ and that he died, was buried and rose again as the scriptures said.  Then he could teach his revelation concerning all that the cross accomplished and the grace of God to us Gentiles.

Hope this helps!