Ey that's the reason I started reading Green Arrow.
First of all, if you haven't read the Injustice comics they are quite enjoyable. Not peak fiction, but they function as fun prequels to the games.
I personally don't know a ton about Zatanna, but there's a relatively recent Reddit post (proxied link) that recommends the recent Dini run and its TPBs as the best place to read. If you want the origin of the character, it seems like you'll have to jump through some hoops. Like Moon Knight, it took forever for her to get a solo run. Unlike Moon Knight, she does not appear to have a convenient omnibus collecting all of her original appearances. If you want her first appearance, it's Hawkman #4 (1964).
Solomon Grundy's first appearance seems to be All-American Comics #61 (1944). He's got a solo run by Scott Kolins from 2009. I see some mentions of Batman: Long Halloween as a good story featuring him, as well.