The following sequence of prayers until Yishtabach (p. 94) is called Pesukei Dezimrah (verses of praise). These selected Scriptural passages were arranged by the Gaonim of the ninth century, in fulfillment of the Talmudic statement (Maseches Berachos 32a), “A person should always praise God first and make his requests [offer his prayers] afterwards.” Beginning with Baruch She'amar (p. 000), it is forbidden to interrupt your prayer with conversation until after the Shemoneh Esrei.
You are permitted to answer Amein, respond to Barechu, Kaddish and to say Kedushah even though you have passed Baruch She'amar. You are also permitted to say Modim d'Rabbonon and the first verse of the Shema together with the congregation.
If you are concerned that the saying of Kerias Shema will not be within the proper time should you follow the regular order of prayers, you are permitted to recite the entire Kerias Shema during the Pesukei Dezimrah.