Having first offered the utmost praise and glorification to Allah, and subsequently invoked prayers and blessings upon the Prophet (peace be upon him) in line with the proper etiquette of making supplications, we then turn our focus towards ourselves and others.
By stating "السلام علينا وعلى عباد الله الصالحين," which is generally interpreted as, "May peace be upon us and on the righteous servants of Allah," we extend our prayers for peace and well-being not only to ourselves but also to all of Allah's virtuous servants.
By supplicating for ourselves first, as in the phrase علينا upon us - we are reminded to begin with ourselves first when making supplications. And with the continuation of وعلى عباد الله الصالحين ‘and upon the righteous servants of Allah’ we fulfill the etiquette of not restricting our supplications to ourselves but rather supplicating for the entire Ummah.
But as we say this we are restricting our supplication, not just to the عباد of Allah - those servants who willingly choose to worship Him out of their free will in this life - but also to the صالِحين amongst them, those who have devoted themselves to Allah, who have humbled themselves in obedience, complying with His commands and avoiding His prohibitions.
This restriction serves as an encouragement for us to cultivate within ourselves the necessary qualities to be included in this category, for if we are, then we will also be included in the supplication of every single Muslim across the world, every time they pray.