To get a feeling for how Dickinson viewed death, just from stanza one, you have to look really closely at the word choices that she uses. For example, she states that death "kindly" stopped for her; her use of the word kind indicates that she did not fear death. She viewed it in a positive light, as a welcome reprieve, as a kindness to have. Death was not a tragedy or an awful thing, but rather a kind thing to someone suffering an illness. Look also at how she capitalizes the name Death; giving death a capital D indicates that she respects death. Think of the words that we capitalize: Your Majesty, God, America, etc. When we capitalize words, it is often a symbol of respect, reverence, and even submission. This shows that Dickinson had a lot of respect for death and what it could do; she showed reverence for its awesome power; she even submitted to that power.
Death picks her up in a carriage; this again indicates that Dickinson feels death is a kind, polite, and respectful power. It didn't jerk her away, dragging and pulling; it didn't yank or jostle her; instead, it kindly placed her in a carriage. A carriage is a courtesy, a pleasant ride through town. This shows that Dickinson viewed death positively, and as a welcome reprieve and rest. One last indication of her feelings for death lie in the fact that the only ones in the carriage were her and death--death cared for her personally, and took the time for her alone. This again shows that he is respectful and kind, not brutal, hurried and impersonal. It was a personal carriage, a personal trip through the town. He offers to gently take her away from her cares.
All in all, the first stanza reflects Death as being a kind, merciful, personal, gentle and polite force in one's life. It is not to be feared, it is not brutal or rough, but a welcome visitor. I hope that helped; good luck!