In Frankenstein, what does Walton want the most out of this stranger?
Letter II, of Mary Shelley's Frankenstein, describes what Walton wants most in life (outside of discovering the "seat of magnetism"). Walton, feeling alone and isolated, although surrounded by his hired men, feels as if no one on the ship understands or relates to him.
But I have one want which I have never yet been able to satisfy; and the absence of the object of which I now feel as a most severe evil. I have no friend.
Once Walton sees the stranger (Victor Frankenstein) he recognizes his sympathy and compassion he feels for the stranger. Walton begins to love the stranger (like "a brother").
I said...I should find no friend on the wide ocean; yet I have found a man who, before his spirit had been broken by misery, I should have been happy to have possessed as the brother of my heart.
As seen in the preceding excerpt, Walton only desires one thing of the stranger--his friendship. Like Walton, the stranger has traveled to the ends of the earth in search of something (Victor's creature and Walton's magnetism). Given that Walton recognizes the stranger's ambitious nature, he knows that the stranger is like him.
Also, in order for the stranger to be his friend, Walton desires the stranger to gain his health as well. Without his health, the stranger would die and leave him isolated again.
In the book Frankenstein Captain Walton has made a friend of the intellectual and sad Doctor Victor Frankenstein. Victor and Walton become very close through the time that they spend together in the freezing climate. Victor becomes sick and his health begins to fade. Walton documents Victor's words and recounts them through his letters home.
The sicker Victor becomes the more Walton feels his loss. He has enjoyed his friendship with Victor and desires to continue the friendship. However, after Victor death and his meeting of the creature he no longer feels the same about Victor and has no further pity of him.