Saratoga has a prodigious literature. Here are a few possibilities (if you run with the first two that should give you an excellent grasp of events)
John F Luzader: Saratoga A Military History of the Decisive Campaign of the American Revolution (by a retired colonel and who used to work at Saratoga NP)
Brendan Morrissey: Saratoga 1777 (The Osprey campaign – now a set book at USMA West Point. Morrissey's work speaks for itself)
John F Elting: The Battles of Saratoga, Philip Freneau Press. (Part of a bicentennial series – Elting needs no introduction but good luck in finding a copy!)
Donald R Cubbison has published a monograph on British Artillery in the Valcour Island and Saratoga campaigns which deals with both material and employment/tatctics. He has also edited Burgoyne's Saratoga papers – a useful primary source.
Michael O Logusz: With Musket and Tomahwk – 2 vols – first dealing with Saratoga and second with the Mohawk Valley campaign. Tried to read this a couple of time and just cannot get into it. Tends to treat myth as fact and obsesses about tomahawks.
W J Wood has Freeman's Farm, Bemis Heights and Oriskany chapters in his Battles of the Revolutionary War but he writes based mainly on secondary sources so is sometimes led astray.
Richard M Ketchum, Walter B Edgar and I think Tom Fleming have all done narrative accounts of the Saratoga campaign.