As mentioned previously, Martian Manhunter was almost never referenced in any way on the covers to the issues of Detective Comics in which the John Jones, Manhunter from Mars strip appeared. That makes the four image cover showcase on the backs of Archive Editions rather lame for fans hoping for a glimpse of this volume's titular star. Tom Hartley solved this problem with his second fan-conceived volume, a Java application that would allow fans to choose their own cover line-up based on individual criteria. I don't expect you'll get a third chance at playing this game, at least until after Martian Manhunter's appearances on House of Mystery covers comes to a bitter end around Volume 5.
The Martian Manhunter Archives Vol.3 back cover web page, as explained by its creator:
Well, I'll darned sure have the cover of the first appearance of Professor Hugo amongst my four entries, even if Tom decided the lead story didn't rate. "I'm inclined not to include the Arnold Hugo story from Detective #306... Poor Arnold Hugo. Bad enough he has two nerd names in one, but he's defeated by his own vanity. "I always said that when I finally met my greatest foe, I would write a tribute to his genius." Would Lex Luthor fall for a line like that?
Since the origin flashback in Detective #322, J'Onn's first battle with Hugo, contains everything Martian Manhunter fans need to know about the villain, I don't think this story needs to be included in the Archives. Instead, my intro to Vol. 4 (which will reprint #322) will contain a synopsis of Hugo's battle with Batman. (To answer your question, I've read all the stories in both Showcase volumes, including the Hugo ones. For the Archive intros, I'm re-reading them.)
Tom's read the story, and saw what came of the Hugo family's exclusion from some fancy-shmancy Gotham City founders event. If I were him, I'd keep one eye on his Archives work, and the other out for genetically engineered tigers the size of houses...