If you are going the collected/trade route, this is the first book:
https://www.amazon.ca/dp/1616557869/?tag=imwanca-20https://www.amazon.com/dp/1616557869/?tag=imwan-20Or this is a larger hardcover omnibus that collects 2-3 of the smaller trades.
https://www.amazon.ca/dp/1506710735/?tag=imwanca-20https://www.amazon.com/dp/1506710735/?tag=imwan-20Here is a reading order for the entire series to date:
Black Hammer, vol.1: Secret Origins
Reprints Black Hammer #1-6 (July 2016 – December 2016).
Black Hammer, vol.2: The Event
Reprints Black Hammer #7-11 & 13 (March 2017 – July 2017 & September 2017).
Sherlock Frankenstein and the Legion of Evil
Reprints Sherlock Frankenstein and the Legion of Evil #1-4 (October 2017 – January 2018) & Black Hammer #12 (August 2016).
Doctor Star & The Kingdom of Lost Tomorrows
Reprints Doctor Star & The Kingdom of Lost Tomorrows #1-4 (February 2018 – June 2018).
Black Hammer ’45: From the World of Black Hammer
Reprints Black Hammer ’45 #1-4 (March 2019 – June 2019).
Black Hammer: Streets of Spiral
Reprints Black Hammer Giant-Sized Annual #1 (January 2017); Black Hammer: Cthu-Louise #1 (December 2018); Free Comic Book Day 2019: Black Hammer #1 (May 2019); World of Black Hammer Encyclopedia #1 (July 2019).
Black Hammer, vol.3: Age of Doom, Part I
Reprints Black Hammer: Age of Doom #1-5 (April 2018 – September 2018).
Black Hammer, vol.4: Age of Doom, Part II
Reprints Black Hammer: Age of Doom #6-12 (October 2018 – September 2019).
Black Hammer / Justice League: Hammer of Justice!
Reprints Black Hammer / Justice League: Hammer of Justice! #1-5 (July 2019 – November 2019).
The Quantum Age
Reprints Quantum Age #1-6 (July 2018 – January 2019).