How is the relationship between Holmes and Watson presented in the first chapter?

In chapter 1, the relationship between Holmes and Watson is presented as mostly a friendly one, but with some less friendly feelings of irritation and insensitivity. It's important to remember that the story is narrated from Dr. Watson's perspective, so we really only have his interpretation of the relationship to go by.
When contemplating whether to say something about Holmes' drug habit, Watson says, "there was that in the cool, nonchalant air of my companion which made him the last man with whom one would care to take anything approaching to a liberty." This suggests that while Watson cares about Holmes enough to feel that he should intervene, the two are not close enough that Watson feels he is able to easily do so. To some extent, Watson also feels in awe of Holmes and "his many extraordinary qualities."
The fact that Watson does, after much hesitation, say something to Holmes about the latter's drug habit, is an indication of how much Watson cares about Holmes. Or, alternatively, his intervention is an indication of how irritated he is by Holmes' habits. It's probably most accurate to interpret Watson's intervention as a sign both of his concern and his irritation.
When speaking to Holmes, Watson calls himself "one comrade (speaking) to another." The implication here is that there is, at least on Watson's side, a brotherly connection between the two.
Later in the chapter, Watson becomes "annoyed" with Holmes when Holmes criticizes his account of a previous case, which Holmes considers too romanticized. Watson is particularly annoyed because he had written the account in such a way as was "designed to please" Holmes. This compounds the impression that Watson rather idolizes Holmes, and also implies that Holmes is, in return, somewhat insensitive, or careless about hurting Watson's feelings.