for a good contained story to read for Batman, i'd go with the stuff by Frank Miller: The Dark Knight Returns/The Dark Knight Strikes Again, and Batman: Year One.

for Constantine, just start with issue one of the Vertigo Hellblazer series-- continuity doesn't really matter, it's just him going after occult stuff issue after issue, but imo the original run is much more contorted and interesting than the ~~~DC Universe Reboot appropriation where the series was renamed to just Constantine and he was aged back down into his thirties, presumably so they could make him act goofier or something, idek.

Ohh dunno why I thought it was on amazon/hbo in my country, so great I will be able to watch it!