I personally like the follow-on comics after the John Byrne series. Reading them properly would take a commitment, though, since they weave a single, almost never-ending, story throughout the different books. These books continue with the character and universe presented in the MoS series: Clark is the real person, Superman the disguise; Jonathan and Martha are still alive; Lex is a business man (when he isn't busy being Clark's nemesis), etc.
A brief, hugely oversimplified, guide to the different eras of Superman. (Note: There is debate about precisely when one age ends and the next begins. I am therefore leaving the cutoffs deliberately fuzzy.)
The Golden Age (1938 until some time in the 1950s): The true origin of Superman. The character is far more rough-and-tumble than he is in modern times. He has no compunction or remorse about killing bad guys or letting them die. This era also includes some cringe-worthy racist and misogynistic attitudes. Still, if you go into the stories with the understanding that they are not of the modern era and if you are willing to look at them as period pieces, they are worth a read.
The Silver Age (some time in the 1950s to ~1970): This is often disparaged as a time of silly stories. The comics in this era were, in general, clearly targeting a very young audience and often had outlandish and highly contrived plots. Superman is the main person, Clark the disguise. Superman becomes increasingly powerful, until he could juggle planets and travel in time by moving really fast (a la the Flash). Nevertheless, there are still some things to recommend the era: It saw many additions to Superman lore including, but by no means limited to, the bottled city of Kandor, Supergirl, and the Fortress of Solitude. It also had some very powerful stories (e.g., The Death of Superman). I enjoy even the silly stories in this age, but only in small doses when I am in the mood to set aside any semblance of logic or verisimilitude for the sake of a fun romp.
The Bronze Age (~1970-1986): Superman's powers were reigned in during the Kryptonite Nevermore series. Clark became a news reporter for Galaxy Broadcasting Company. The stories were often still quite fantastical, but seemed to target a somewhat older audience. It ended with the powerful and controversial two-part series "Whatever Happened to the Man of Tomorrow?" This ended the Golden/Silver/Bronze age Superman immediately preparatory to the first Superman reboot. (Byrne's "Man of Steel" series.) It's a story worth reading, but only after you are very familiar with the Bronze Age Status Quo.
The Byrnes and post-Byrnes Era (1986-2011): I highly recommend the books from the start of this era. The quality declined toward the end.
New 52 Era (2011-2016): I wouldn't recommend.
Rebirth Era (2016-last month): Highly recommend
Current era (starting with a new series, also titled "Man of Steel" that will start publishing later this month): ???
Sorry the ending here is so abrupt. I just realized I am late for work.
Happy Reading,
Lynn
