As you note, the Joseph Smith-History in the scriptures is a good resource to get started with. It reminds us of the core reason why Joseph’s life is worth examining: he was a prophet of God, chosen by Him. But it only covers the earliest events in Joseph’s life and ministry. For a continuation on this theme, you can read the entire Doctrine and Covenants to get a sense of the voice of the Lord through Joseph (again, this is why he’s so important to Latter-day Saints).
From here, you can get into the uncanonized sermons and writings of Joseph Smith. The most accessible is probably Teachings of Presidents of the Church: Joseph Smith – the instruction manual the Church produced of his life and teachings. The chapters are grouped by topic for easy reference. Additionally, you may consider reading Teachings of the Prophet Joseph Smith. This was compiled and edited by Joseph Fielding Smith and is organized chronologically. I recently finished rereading it and am once again impressed by how well Joseph understood doctrine – specifically that of Priesthood and where Adam, Elijah, and the Temple come into play. The similarly named Discourses of the Prophet Joseph Smith by Alma P. Burton is something of a cross between the two. It groups Joseph’s discourses topically rather than chronologically, but is “fuller” (for lack of a better term) than the Church manual.
For more of a biographical sketch, you should start with The History of Joseph Smith by His Mother by Lucy Mack Smith. It’s really a history of the Smith family, but you get to see Church history and Joseph’s own life through a mother’s lens. May we all be viewed thus. For a more scholarly approach, you can read Rough Stone Rolling by Richard Bushman. If you decide to read this, I highly recommend getting comfortable wading through footnotes as he includes a number of sources that I find questionable. For contemporary accounts of Joseph, you can read Remembering Joseph, edited by Mark L. McConkie. It’s a collection of public and private recollections of people like Brigham Young, Hyrum Smith, and others.
But if you enjoyed the Joseph Smith-History, you might consider reading the first volume of History of the Church compiled by B.H. Roberts. The first volume is more narrative in structure than the other volumes and opens with the section excerpted into Joseph Smith-History. A more modern look at the same sources can be found in the Joseph Smith papers – available in book form and online.