That's actually kind of a difficult question. There aren't really any histories that I would recommend without qualification. Every history has its good and bad aspects.
I'm not sure what you're looking for, but a few things come to mind. You might try some of Mark Noll's books like his 'History of Christianity in the United States and Canada'. I've listened to him speak and I think he's a pretty decent and thoughtful historian. A lot of partisan historians dislike him with I consider to be a positive sign.
There are some broader Church histories that deal with the American Church but are by no means exclusively American. Erdman's 'Handbook to the History of Christianity' gives a good broad overview and certainly includes America toward the last quarter of the book.
'Sketches From Church History' by Houghton and 'The Church in History' by BK Kuiper cover a lot of American history and aren't too complicated, but both of these books are very biased toward the Reformed wing of Protestantism. I like these books and have read and re-read them but at the same time they can really irritate me. That's how most histories are.
If you want to get really in depth and deal with reading primary sources I recommend 'American Christianity: An Historical Interpretation With Representative Documents' by Smith, Handy, and Loetscher.
That's pretty heavy reading, very tedious but good and necessary if you want to do some real research.
It's a controversial book but very interesting, Butler's 'Awash in a Sea of Faith' re-casts American Church History. He upsets a lot of people and undoubtedly gets some things wrong, but he challenges the Puritan-centered view of early American Church history and its role in the formation of American culture. American Romanticism in the 19th century picked up on the Mayflower Pilgrims as iconic and representative of the spirit of America, but this was propaganda. And both the public and the Church in general are confused about what the Pilgrims actually were about.
My own positions are very close to the Separatist Mayflower Pilgrims. But Plymouth ultimately failed and was swallowed up by the Puritan Massachusetts Bay Colony which started in 1630. The Pilgrims though captivating and iconic have almost nothing to do with American Church History. Roger Williams though a Baptist, in many ways carried on their legacy but this too was lost in time. Today most Baptists in America find their cultural impulses from the Puritan/Reformed wing of Christianity even if they would be quick to deny it. Historically they may want to identify with the Anabaptists and they think they find commonality with the issue of Baptism. But that's really about as far as it goes. Most Baptists in the United States have almost nothing in common with Anabaptism and its rejection of power and Sacralism.
Butler focuses more (and I think rightly) on Virginia. Other historians like Hackett Fischer have focused on Virginia as really being the cradle of Colonial America and much of its culture. This is not to downplay what was happening in say Georgia, Pennsylvania or New England, but Virginia just dominated in so many ways as the people branched out and headed to Kentucky, Ohio, the Ozarks and the Prairie.
But the Virginia story has never been as appealing to the 'Christian America' crowd until recent years when due to the Culture War these folks have shifted and embraced both historical Anglicanism with its Imperial ideals and even Roman Catholicism.
Butler rightly brings out the Enlightenment influences which were considerable in Virginia especially in the 18th century and the events leading up to the American Revolution.
A lot of Christians hate this book but if you want to get the picture you have to read widely.
Another interesting read is 'Without God, Without Creed: The Origins of Unbelief in America' by Turner. He delves into the growth of unbelief and secularism in American culture which was well underway before the Civil War and before Darwin. Again, it won't please the David Barton school of American Mythology but it helps to give a full orbed view of what was happening in our very complex culture. Turner's work doesn't sound like a Church History but in a way it is.
I've not read The Religious History of America: The Heart of the American Story from Colonial Times to Today by Gaustad and Schmidt, but I've heard pretty good things about it.
If this is something new, then get a good 'overview/survey' book like Noll or Koester's 'History of Christianity in the United States' just to familiarize yourself with the people, places, movements etc.... Then you can start going back and delving into more complicated and in depth histories.
It's good to also just familiarize yourself with American history in general, the movements of people and the culture etc... It's a huge book but Albion's Seed by Fischer is a fascinating look into American cultural history. I've enjoyed reading it cover to cover and picking it up as a reference. His follow up 'Bound Away: Virginia and the Westward Movement' is shorter (366 pages) and both summarizes Albion's Seed and expands on it.
In Albion's Seed he focuses on four major British folk cultures at work in America...the East of England/Puritan culture, the West Country/Virginia culture, the North of England/Quaker culture and the Borders and Ulster/Scots-Irish culture.
It's a reductionism as any such attempt a categorization is bound to be but he's using these as a broad cultural categories... folkways. He does a good job even if he doesn't always get everything quite right. The problem with the book is at just under 1000 pages....it's way too short.
In Bound Away he expands this and covers early German culture in America and African-Americans as well. I find that understanding the culture and the movements of peoples helps me to better understand Church History.
At one point in time I was focusing almost exclusively on Church History but I found that you almost have to read 'secular' history alongside it. In fact they are inseparable. I used to feel a little guilty for reading a secular history book, like it was a waste of time.
But then I realized learning history is never a waste of time and history is the great umbrella wherein we are exposed to every facet of knowledge and by opening up these worlds we learn of new ways to apply the Bible, we're presented with new problems and ideas which we must filter through the lens of Scripture. In fact by focusing exclusively on the ecclesiastical and theological aspects of history we will grossly misread and misunderstand what was happening.
Many Christians rail against interpretations of the Reformation that cast it in sociological terms. That's a mistake but it's an equal mistake to only see it in religious terms and miss the political and social aspects of what was happening in 16th century Northern Europe.
We have to read both secular and Church history and that's a real stumbling block for some Christians who are unwilling to read anything not written by a Christian. The doctrine of Common Grace has certainly been abused and misused but should not be wholly rejected.
Reading secular history can be challenging, even to our faith at times, but unlike many Fundamentalists I find that to be healthy. And I say that as one who would be labeled as a Fundamentalist by most people.