I can't find a reputable history on early american Mormonism, but I would really like to learn more about the history around the movement.
The field of early Mormon history is filled with faithful history, written by believers and critical history that believers would call "anti-mormon". For example, Rough Stone Rolling is a highly respected biography of Joseph Smith written by an quality historian but that historian is still a believing Latter-Day Saint. I'll give you an example of the differences. When describing Joseph's use of a seer stone to locating buried treasure Bushman describes these activities as Joseph's prophetic training and he is developing the skills needed to later use that stone to translate the Reformed Egyptian writing for the Book of Mormon. A secular historian doesn't begin with the a priori assumption that magic rocks exist in the world and people may need to train to use them. In choosing a naturalistic description of Joseph's behavior the reader may see that as an attack on Joseph's credibility as a prophet.
The one book that I believe reasonably walks the line between the two would be Michael Quinn's Early Mormonism and the Magical World View
This book is specific to Joseph Smith, but No Man Knows My History: The Life of Joseph Smith is fantastic.
If you are at all interested in the international spread of mormonism in the 19th/c I would definitely recommend "Chosen People, a Promised Land: Mormonism and Race in Hawai'i" by Hokulani Aikau. Pretty interesting account of how non-Americans understood their place and role in an American centered religion and how missionaries in 1850 (only 20 years after the founding of the church), had already gone abroad with their message and what it meant to the people they missionized and how they dealt with some of the church's early racial policies.
As part of the Oxford History of the United States Series, Daniel Walker Howe wrote a book in 2007 entitled What Hath God Wrought: The Transformation of America 1815-1848. In it, he has several sections on early Mormonism.
Here is his statement on Mormon history sources from his bibliographical essay: Historical literature on Mormonism is gigantic and sometimes polemical. Insightful presentations of the Mormon religion by outsiders include Thomas O’Dea, The Mormons (1957); Jan Shipps, Mormonism (1985); and Paul Conkin, American Originals (1997), 162–225. The projected multivolume history by Dale Morgan was cut short by his death; what little we have appears in Dale Morgan on Early Mormonism, ed. John Phillip Walker (1986). Quite a few fine historians are Latter-day Saints, and some of them write about Mormon history; see, for example, Leonard Arrington and Davis Bitton, The Mormon Experience (1979); Klaus Hansen, Mormonism and the American Experience (1981); Grant Underwood, The Millenarian World of Early Mormonism (1993); and Richard Bushman, Joseph Smith: Rough Stone Rolling (2005). Additional biographies of Joseph Smith, each with its own viewpoint, include Fawn Brodie, No Man Knows My History, rev. ed. (1973); Robert Remini, Joseph Smith (2002); and Dan Vogel, Joseph Smith: The Making of a Prophet (2004). Mormon and gentile historians collaborate in an anthology, The New Mormon History, ed. D. Michael Quinn (1992). On the cultural matrix of early Mormonism, see D. Michael Quinn,Early Mormonism and the Magic World View (1987); John Brooke, The Refiner’s Fire (1994); and Terryl Givens, The Viper on the Hearth (1997). Stephen LeSueur, The 1838 Mormon War in Missouri (1987) is judicious. The Mormon trek to Utah is portrayed in Leonard Arrington, Brigham Young: American Moses (1985); Klaus Hansen, Quest for Empire (1967); and Marvin Hill, Quest for Refuge (1989).
Your question is difficult to answer. As others have said, Mormon history is intricate and people are frequently biased concerning their presentation of the history. You will likely need to read multiple sources to get an accurate representation concerning early Mormon history. If you really want to get to know early Mormon history I would start with B.H Roberts "A comprehensive history of the church." B.H. Roberts was a high leader in the LDS Church; however, for being a member and leader he presents an okay view. For example, he discusses Joseph Smith's use of the rock in a hat, which most books written by active Mormons shy away from. In addition, he wrote a book that highly questions the authenticity of the Book of Mormon. So, I think he tried his best to be objective. His history of the LDS Church is not for the faint hearted though, it is five volumes long. After you read that work, you can read some books on more specific topics concerning Mormon history written by such people as Jerold and Sandra Tanner, D. Michael Quinn, and Grant Palmer.