Personally, there are quite a few of those DC recommendations that I personally would not recommend. Mainly the ones with characters from long running titles that were just sort of forced into rebooted DC continuity rather than when they were previously under Vertigo and a) existed entirely outside of DC or b) in the early transition era, had only very loose connections if any that still allowed them to be very standalone.
That said, if you are a big fan of the ongoing Vertigo Hellblazer series, I would personally avoid the later N52/DCYou/Rebirth eras of Constantine. It’s not the same and you probably won’t get much out of it. Very diluted and with writers that never felt right for the character. The NEW Black Label (aka/ formerly still Vertigo) series by Si Spurrier is actually REALLY great and feels like a return to the real Vertigo Hellblazer, but alas, Black Label and will probably never be on here.
The N52 Animal Man and Swamp thing were actually pretty good in their own way. Different, but still worthy reads. I think they really wore their welcome quickly. By the time the Rotworld crossover came around they both felt a little tired. Might feel better reading everything through in a few sittings though.
Starman, and the Young Animal and Wildstorm titles (Especially Planetary and Sleeper) are all great recommendations! Madame Xanadu, House of Mystery, and Flex Mentallo, all are or technically are Vertigo titles, so I wouldn’t count those as recommendations. I’d also sort of throw Doom Patrol (1987) from Morrison’s run on in there by default.
I think the Kelley Jones’ couple of Deadman mini-series had a strong Vertigo vibe but were just published under DC. I’m a huge Vertigo fan and wish we had a lot more of it on DC Universe that the minimal amount that DC Universe includes (Or wants to even acknowledge?).