I'd recommend picking up the first issues of any of these DC comics:

Bat Mite
Batman Beyond
Bizarro
Black Canary
Constantine The Hellblazer
Doomed
Dr. Fate
Green Lantern The Lost Army
Harley Quinn & Power Girl
Justice League of America
Martian Manhunter
Midnighter
Omega Men
Prez
Red Hood Arsenal
Robin Son of Batman
Section 8
Starfire
We Are Robin

They are all completely brand new, so new that they haven't even been released yet. They will all be released throughout June, which is very close now. You don't really need to know anything prior to get into them, and you'll be following many brand new comics from the very beginning!

One DC series I would highly recommend to you is Gotham Academy. The seventh issue comes out next month, along with the first trade paperback collecting the first six issues. If you like the art style of manga, I think you would definitely enjoy Gotham Academy.