Time for a minor total-comics-dork divergence here.
As much as I love Vertigo's reinventions of superheroes, there is one thing about them I can do without: they make comics fans assume that the original sucked without bothering to check. It is just sort of assumed that they must have been "four-color trash", whatever that happens to mean to the individual in question, before the British geniuses got their hands on them.
Animal Man is probably not the best choice for me to leap to the defense of, since he was always pretty goofy. That said, goofy doesn't mean necessarily bad. His early adventures were a lot of fun to read, and if they hadn't been, Morrison would probably have never bothered with him; he specifically asked to reinvent his favorite old character who had fallen into Comics Limbo. To me, it's more irritating in the cases of Swamp Thing and Doom Patrol; Moore and Morrison's respective runs on those were genius comics, but the original runs were also excellent comics that a lot of comics fans automatically discard as Less Than Trash for not being the Vertigo reinventions.
Vertigo eventually made a formula out of miniseries that 'reinvented' minor Silver Age characters by adding experimental layouts and psychological dysfunction. Some of these series were quite good (Human Target) and some were quite bad (Dr. 13), but the effect they mostly shared was to bring the obscure characters into fan consciousness as "wacky old crappy old characters who were redeemed by Vertigo" no matter what the original character's quality might have been.
(Fanboy rant mode: off)
Anyway, Morrison's Animal Man is really good and you should read it. Although the farther you get into the run, the more it relies on certain plot elements from other superhero comics and inspects the state of the industry as a whole at the time. I dunno how accessible that part of the run would be to most readers.