My advice is not to limit yourself to recent stuff. DC has a long and rich history to choose from, and some of the bad decisions they’ve made in the last eight years or so have been piling up. Of course, stuff from before a certain point tends to have very clunky writing and less polished inking and coloring, so a new reader might be put off, but if you stick to the late '80s on, you’ll be doing alright on writing, and while the quality of the art depends more on the penciler, you start to see more detail on the coloring sometime in the late '90s.
Some good, beginner-friendly series and stories for the characters you mentioned:
Batman: This is my strongsuit, so I have a few different ways you could approach it.
-It has some detractors, but Batman: Hush (1941 Batman series, starting somewhere around issue 612 from 2004) is a really solid, self-contained sort of “tour” of the supporting cast and rogues gallery and while the mystery isn’t super difficult, there are some good twists to it.
-If you want a longer sequence of stories that’ll introduce you to other series and Bat-Family members, you can go crossover-hopping through the timeline with Year One, The Killing Joke, A Death in the Family, Knightfall/Knightquest/Knightsend, Prodigal, Troika, Contagion, Legacy, Cataclysm/Aftershock/No Man’s Land, Officer Down, Bruce Wayne: Murderer?/Bruce Wayne: Fugitive, Hush, War Games, Under the Hood, and RIP.
-Finally, you could also look into the prequel stories that address Batman’s early years: Year One, Year Two, Year Three, most of the early arcs of Legends of the Dark Knight, The Long Halloween, Dark Victory, Robin: Year One, Batgirl: Year One, Nightwing: Year One, and Catwoman: When in Rome.
Nightwing: The 1996 series is fantastic up until issue #80 or so. When you get there, do yourself a favor and stop. Also look into the 1998 Titans series.
The Flash: Try starting around issue #62 of the 1987 series. Mark Waid’s run created most of the franchise’s lore, and the guy’s plots are genius.
Aqualad: Can’t really help you here. Maybe the Young Justice comics (not the '98 series, the 2012 tie-in for the cartoon; the '98 series is great, it’s just not related to the cartoon in the slightest and doesn’t have Aqualad)?
Black Lightning: I honestly don’t know much about him. I can’t help much here, unfortunately.
Superman: Superman’s history and continuity aren’t my strong suit either, but the 1986 miniseries “The Man of Steel” is quite good.
Cyborg: His history got kind of complicated at a certain point, but I’d say try either New Teen Titans starting in 1980 (introduced the character, but the dialogue and narration are kind of painful for most of the run) or Geoff Johns’ 2003 Teen Titans (which I haven’t read but people seem to like).