The war by itself is a far less interesting affair than how it happened, and what made the country be OK with fighting. For that you need to start at the end of the previous dictatorship, and cover the entire 2nd republic. Then the war starts making sense.

So I'd read The Collapse of the Spanish Republic, by Stanley Payne. He was a journalist in Spain through the entire period, so most of what he does is provide a first hand account. He never claims to try to be impartial, but he's pretty nouanced, as he knew a lot of the players personally.