From that specific promotion it may be a little tricky to have beginner-oriented recommendations because of the specific publisher restriction, unfortunately, sorry!
I don’t recognize anything from the current publisher, ホビージャパン, for example.
It only lists the next upcoming publisher for now, and it’s コアミックス. I don’t see any of the usual beginner recommendations in their lineup either, but you might get a kick out of Fist of the North Star if you happen to like extremely over the top 80s action (it doesn’t appear to have furigana but dialogue probably isn’t especially critical to understanding the story so maybe it would work ok), and I haven’t read City Hunter but I get the impression it’s a classic, in an again, very 1980s sensibilities sort of way (and it does appear to have furigana).
I would honestly probably most recommend just checking out the Absolute Beginner Book Club or Beginner Book Club picks, seeing if any of those catch your eye, and then marking them on bookwalker with the check mark next to the cover of the book, so they’ll be added to your checklist and appear in the
Check！した作品の中にセール作品があります (if its on sale) or
Check！した作品の中にコインUPの作品があります (if it has coinback) sections of the menu reached via the " 
Check!" in the top right corner of the bookwalker page when a promotion comes up.