Pesukei d’Zimrah are to be recited in a relaxed manner and not hastily (Shulchan Aruch 51:8).
Baruch She’amar possesses a special virtue and alludes to sublime matters; therefore, it is customary to recite it while standing (Mishnah Berurah 51:1, Kaf HaChaim 1). According to the Ashkenazic minhag, one also stands while saying Yishtabach, which ends Pesukei d’Zimrah. However, according to the Sephardic minhag, one need not stand (Rama 51:7; Kaf HaChaim 42).
Likewise, it is customary to stand for Vayevarech David until the words “Asher bacharta b’Avram,” out of respect for the Kingdom of Israel founded by King David.
After learning that one of the two reasons for the recital of Ashrei (Psalm 145) is the mention of the verse, “Pote’ach et Yadecha,” (“You open Your hand and satisfy the desire of every living being”), we understand why this verse must be said with kavanah. If it is recited without kavanah, it must be repeated. Even if one already started reciting other passages, he must say that verse again with kavanah because it is the most important part of Pesukei d’Zimrah. Some say that since he did not have kavanah for that main verse, his recital of the rest of the Psalm is not considered valid either, and he must go back and repeat from “Pote’ach” until the end (Mishnah Berurah 52:16). However, according to most poskim, it is enough to go back and recite only the verse “Pote’ach” by itself (Shulchan Aruch 52:7).
.According to the Sephardic minhag, “Hashem Melech Hashem Malach…” is recited twice before Baruch She’amar, and on Shabbat and Festivals it is said while standing. Beit Yosef 50 writes in the name of Shibolei HaLeket 76 that the reason is based on the Midrash which states that the angels said it while standing. However, on weekdays, since people did not have leisure time because of work, they were not accustomed to standing. Nowadays, it is customary to stand even on weekdays.