The tone of The Fellowship of the Ring really varies from Book 1 to Book 2. In Book 1, we get plenty of funny dialogue and homey expressions. Take, for example, Tolkien's presentation of Bilbo's birthday party speech:
I shall not keep you long, [Bilbo] cried. Cheers from all the assembly. I have called you all together for a Purpose. Something in the way that he said this made an impression. There was almost a silence, and one or two of the Tooks pricked up their ears. (1.1.58)
Bilbo's audience is ready and eager to cheer a short speech by Bilbo (though they aren't too eager to hear a long one). But Bilbo clearly knows something they don't, which lends a somewhat hard edge to his birthday celebrations. Nonetheless, the general tone of these early chapters of the novel is quite homey. There are no long words or Elvish names, and none of the language is difficult to understand. Even the first major adventure Frodo and his friends experience in the wider world is quite cozy: Tom Bombadil's cottage is small and pleasant, and the man himself spends most of his time singing his little rhyming songs much as the Hobbits themselves do. Two peas in a pod.
The tone of the novel really starts to change with the introduction of Aragorn: he is mighty serious about the quest and his songs are much less lively. Once Aragorn comes into the picture, the Hobbits make it to Rivendell and to a council of the wise of Middle-earth. Surrounded by these elevated figures, the earlier, homey tone of the book starts to shift to something grander and more melancholy. After all, the Shire may be a comfortable place, but it is now far behind Frodo, Sam, Merry, and Pippin. Instead, they are four tiny Hobbits surrounded by towering, beautiful Elves and unbearably wise Wizards and men.