First, you need to be familiar with both universes. Read the Harry Potter books and watch the movies, and do the same for Deadman Wonderland. Then, decide on a central plot. It could be a crossover where characters meet, or it could be a more complex story where the worlds start to merge. Create new characters if necessary, and make sure to keep the tone consistent with both series.
A dark wizard who has merged the dark arts with Wonderland's magic could be the main villain. He might have created some sort of dark Wonderland where all the creatures are under his control, and Harry has to break this control to restore balance.
One interesting plot could be a time - travel story in the Harry Potter wonderland. For example, a character goes back in time to the Marauders' era and gets involved in their adventures, while also trying to prevent a future disaster in the wizarding world. Another idea is a story where a new, powerful magic is discovered in the wonderland, and Harry and his friends have to figure out how to control it before it falls into the wrong hands. A third plot could be about an alternate reality where Voldemort won the war, and the remaining good characters have to find a way to reverse the situation in the harry potter wonderland.
In some fanfiction, Harry could be the one who enters Wonderland. Maybe he's on a quest there, and he meets the Cheshire Cat. The Cheshire Cat could guide him, but in a very mysterious way, just like how Dumbledore often gives cryptic advice to Harry. Harry would have to adapt his magical skills learned at Hogwarts to the strange magic of Wonderland.
A Harry Potter - Deadman Wonderland fanfiction could focus on the concept of magic vs the extreme and cruel system of Deadman Wonderland. The wizards might be seen as a threat to the order of Deadman Wonderland, and the Deadman Wonderland characters might be in awe or fear of the magic. There could also be a plot where a character has to combine the magical knowledge from Harry Potter with the survival skills needed in Deadman Wonderland to overthrow the corrupt system in Deadman Wonderland.
One idea could be Harry finding a hidden portal in Hogwarts that leads him to Wonderland. There, he meets the Cheshire Cat who helps him understand some of the mysteries of the wizarding world in a different way. Maybe he has to solve Wonderland - like riddles to get back to Hogwarts.
Definitely Harry Potter. Since he's the main character of the original series, many fanfiction writers like to put him in new situations, whether it's facing a new dark wizard or exploring a different kind of magic. Hermione is popular too. People are interested in her intelligence and how she might use it in various scenarios not covered in the books. Ron Weasley also has his fans in the harry potter wonderland fanfiction world. Writers might explore his growth as a wizard and his role in different adventures, especially when it comes to his loyalty to his friends.
A really interesting plot would be if the characters from Alice in Wonderland were students at Hogwarts. Alice could be in Gryffindor, always getting into strange adventures around the school that remind her of Wonderland. The Mad Hatter could be a Potions master who makes the most bizarre potions. And the Red Queen could be a strict teacher who is always trying to catch students breaking the rules. There could also be a plot where Voldemort tries to take over Wonderland for some dark purpose, and Harry and his friends have to stop him there.
A great fanfic idea could be a crossover where Voldemort tries to take over Wonderland. The characters from Wonderland, along with the help of the 'Harry Potter' gang, have to fight against him. The magical creatures in Wonderland, like the Jabberwocky, could team up with the magical creatures from the 'Harry Potter' universe, such as hippogriffs, to defeat Voldemort.
Hermione is quite common. Her intelligence and inquisitive nature make her a great fit for exploring the strange world of Wonderland. She could analyze the different creatures and situations she encounters.