All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no evidence for this sequence when supplicating, namely that a person should first supplicate for himself, then for his parents, then for his brothers and then for other people as you mentioned in the question. Rather, this varies and depends on the circumstances and purposes. One is to prioritize what is appropriate for the circumstance and the purpose for each invocation accordingly.
If there is no reason that requires prioritizing some people over others, then it is preferable to begin by supplicating for oneself, then one's closest relatives, like parents, wife, children, siblings and others, and then for the Muslims in general. If one begins with some before others, there is nothing wrong with it.
Allaah Knows best.