In Chapter One of The Lord of the Rings, what is Gandalf's reputation?
In Chapter 1 of The Lord of the Rings: The Fellowship of the Ring, we are given Gandalf's reputation from the point of view of the hobbits. As we see throughout the first chapters, the hobbits are so insular that their view of the world, and their understanding of their place in it, is naïve and childlike. The reputation of Gandalf among them is similar in that it focuses on just the aspect of him that they know.
To the hobbits, Gandalf is a curiosity. They have a vague sense that he is more than a mere man, and they know that the stories of him go far beyond the memory of any living hobbit. However, as the narrator reveals to us, the hobbits have no idea of his labors in the wider world.
Thus, the hobbits lack the awe of Gandalf we see later in the books. In the same vein, they also do not see him as a harbinger of trouble the way other societies do. Rather, they see him as a purveyor of amusements. They are excited to see his fireworks, which are legendary among the hobbits, although they have not been seen in living memory. They do not worry that his presence may foretell darker happenings. At that point, only Bilbo knows that the seemingly kindly and harmless old man is far more than a simple conjuror.
Though in the cinematic version of The Lord of the Rings, Gandalf is labeled as "a disturber of the peace," in the first chapter, we also Gandalf through Bilbo's eyes, where he is first labeled "the great Wizard" (which, using the article "the" instead of "a" shows the amount of respect Bilbo has for Gandalf and his power).
Amongst other hobbits, however, Gandalf's reputation is varied.
The miller labels Gandalf as "that old wandering conjuror," and believes that the "queerness" from Bilbo and Bag End are a result of Gandalf's influence. Other hobbits only associate Gandalf "to his skill with fires, smokes, and lights," undermining the respect and knowledge that Bilbo has, being his friend and understanding the more dangerous and difficult reality of Gandalf's wanderings--especially considering Bilbo took a very main role in one of those adventures, back in events of The Hobbit.
For most of the general public, however, Gandalf is mostly legend and his coming to the party creates an anticipated excitement. Though they'll get to experience the wonder of his fireworks, many of the general hobbit population will never understand the true depth and effect of his power, seen throughout the series.
Quotes Pulled from online source, found here: http://portal.tolkienianos.pt/files/The_LotR_I.pdf