Reddit reviews The Last Testament of Lucky Luciano: The Mafia Story in His Own Words

Seconding the recommendations on Rothstein and Boardwalk Gangster (though I believe Boardwalk Gangster isn't the same as The Real and Fake Gangster; if I remember right Boardwalk Gangster is updated with new research and details, so I recommend getting that one) and adding a few more recommendations; to round out the New York gangsters, there's Little Man:
http://www.amazon.com/Little-Man-Meyer-Lansky-Gangster/dp/0316511684/
and while I also haven't read anything about Capone, Prohibition Gangsters gives a decent overview of, well, prohibition gangsters in general (including Capone), though being a summary it doesn't go into as much detail as it could on stuff like the Castellammarese War. Still, it's a good starting point:
http://www.amazon.com/Prohibition-Gangsters-Rise-Fall-Generation/dp/0813561159/
As far as I'm aware there's not a book on the Castellammarese War or the entire period in general, which is a shame. There is The Mob and the City, which looks at the genesis of the Mafia until Apalachin specifically within the context of New York City; it's one of the only books that covers as wide a span of time as it does, but I recommend it with some reservations. It's very revisionist and in my opinion doesn't give Luciano the credit he deserves, plus it focuses VERY heavily on the Mafia specifically and (despite Meyer being on the cover) ignores the contributions of non-Italian organized crime figures like Rothstein and Lansky, which is kind of annoying if you know how much involvement they actually had:
http://www.amazon.com/Mob-City-Hidden-History-Captured/dp/161614923X/

I'd also recommend getting your hands on The Last Testament of Lucky Luciano and Mogul of the Mob, if you can. There are some issues with how reliable they are, considering how involved Luciano and Lansky were in their publication (and there are additional, somewhat notorious issues surrounding The Last Testament especially), but they're very good reads for entertainment value alone, and there is some truth to at least SOME of the things they talk about. Mogul of the Mob tends to be a bit pricey, but The Last Testament got a relatively recent reprint and ebook publication so it's easy to get ahold of:
http://www.amazon.com/The-Last-Testament-Lucky-Luciano/dp/1936274574/
http://www.amazon.com/Meyer-Lansky-Mogul-Dennis-Eisenberg/dp/044822206X/

Basically until someone writes a definitive reliable single volume on the era, you kind of have to piece stuff together from various sources, which can get kind of expensive depending on how in depth you want to go, but it's all fascinating stuff.