Raven and Catwoman are both playable characters in the game. It's on PS3, Xbox 360, and Wii U. I reccomend getting it for Xbox or Playstation if possible because for some reason NRS (creaters of the game) doesn't show much love for Wii U.
Here's a quick list of the 30 playable characters in the game:
Well I only have it for Xbox so I can explain the buying thing to. For Xbox you need 400 Microsoft Points ($5). If you don't know how to obtain Microsoft Points you can buy some in the store for a certain amount of money $5-400 MSPs, $20-1600 MSPs, etc. Once you've entered the codes for the points you can either:
1. Go to the Xbox Marketplace. Go under Injustice and buy your DLC there.
2. Go into the game, select bonus features, select downloadable content, select buy and all the downloadable content will be there.
There is also DLC skins. ($3 for a pack) ($1 for a single skin) ($0 compability skin)
Here are the skin packs:
Arkham City skin pack- Batman, Joker, Catwoman.
Red Son 1- Superman, Wonder Woman, Solomon Grundy.
New 52- Superman, Batman, Wonder Woman.
Teen Titans- Deathstroke, Cyborg, Raven.
Bad Girls- Wonder Woman, Catwoman, Harley Quinn.
Blackest Night 1- Superman, Flash, Doomsday.
Red Son 2- Batman, Green Lantern, Deathstroke.
Earth 2- Flash, Hawkgirl, Solomon Grundy.
Blackest Night 2- Aquaman, Hawkgirl, Batman.
Flashpoint- Aquaman, Wonder Woman, Deathstroke.
Ame-Comi- Wonder Woman, Catwoman, Harley Quinn.
iOS (i'll explain at bottom).
Man of Steel- Superman.
Blackest Night- Batman.
John Stewart- Green Lantern.
Containment Suit- Doomsday.
iOS skins are from the Injustice app that is available for apple pruducts (also Android this fall). In the app you can do certain challenges that can unlock skins for the console version of the game. You have to have a WB account and connect your account to your console and phone. These skins are- Batman Beyond, Knightfall Bane, New 52 Green Lantern, Lockdown Superman, New 52 Flash, and Arkham City Harley Quinn. If you have the Wii U version of the game then you can buy the pack but if you have Play Station or Xbox then you have to unlock them through doing the challenges. New 52 Flash is unlocked by connecting your WB account to your console and phone.
I hope this helped with all the DLC for Injustice at the moment. If this raised more questions then I would be happy to try to simplify it for you.