You would probably be better off picking up issues collected in graphic novel/trade paperback/omnibus form, especially since you said your SO isn't interested in collecting. Superboy, Batman, and Justice League are all popular, long-running series with hundreds of issues which is both prohibitively expensive and takes up a lot of space.

It also depends on which iterations your SO is most into. Superboy is a title that's been held by multiple characters (Clark Kent, Conner Kent, Jon Kent, etc), the same goes for Batman (Bruce Wayne, Dick Grayson, John Paul Valley, etc), and the Justice League cast is a rotating ensemble.

You can check the sidebar for recommendations but here are a few I'd recommend to get you started (my Superboy knowledge is very limited so take those with a grain of salt):

Superboy:

• Superboy and the Legion of Super-Heroes
  
  
• Superboy: Boy of Steel
  
  
• Superboy: Smallville Attacks
  
  
• Superboy: Trouble in Paradise
  
  

  Batman:
  

  
  

• Arkham Asylum: A Serious House on Serious Earth
  
  
• Batman by Morrison Omnibus Vol. 1 & Vol. 2 (or the smaller trade paperbacks)
  
  
• Batman by Snyder/Capullo Omnibus Vol. 1 (or the smaller trade paperbacks)
  
  
• Batman: The Black Mirror
  
  
• Batman: The Dark Knight Returns
  
  
• Batman: Hush
  
  
• Batman: The Killing Joke (definitive Joker story, and a partial basis for the recent film)
  
  
• Batman: The Long Halloween
  
  
• Batman: The Man Who Laughs
  
  
• Batman: White Knight
  
  
• Batman: Year One
  
  
• Gotham Central (or the smaller trade paperbacks)
  
  

  Justice League:
  

  
  

• DC: The New Frontier
  
  
• JLA: Rock of Ages
  
  
• JLA: Tower of Babel
  
  
• Justice
  
  
• Justice League: Darkseid War
  
  
• Justice League International
  
  
• Kingdom Come

Death in the family is the death of a robin, death of the family is joker tormenting batman. You would also love this one:https://www.amazon.com/Arkham-Asylum-Serious-House-Earth/dp/093028948X