Well, 'A Murder of Crows' is a must - read. It shows the complex relationship between Swamp Thing and the creatures in the swamp. Also, 'Down Among the Dead Men' is really good. It dives deep into the horror aspects of the Swamp Thing world, with great art and a chilling story.
Definitely check out 'The Saga of the Swamp Thing'. It has a lot of important elements that introduce new readers to the whole concept of Swamp Thing. And 'Tales of the Green Lantern Corps' which has some crossover stories with Swamp Thing that are both fun and informative for those new to the character.
One great fanfiction could be about Swamp Thing and Poison Ivy teaming up to save a dying forest. Their combined powers of nature could create an interesting dynamic in the story.
The synopsis of Swamp Thing in the new DC Universe could be really exciting. Swamp Thing is likely to be a complex character. His story could begin with a mystery in the swamp. There could be disappearances or strange phenomena. As he discovers his powers, he realizes he has a role to play in protecting not just the swamp but also the entire ecosystem that is connected to it through the Green. He may face villains who want to use the power of the Green for their own evil purposes, like creating some sort of mutant plant - human hybrids to take over the world. And throughout his journey, he has to come to terms with his new identity, which is part plant and part human, and find a way to coexist with the humans who are often afraid of him.