First I'll say I'm sure you'll love the X-23 back stories. Great art, great story, and is new reader friendly. With no knowledge of the character i read the books and jumped right into New x-men and other books.
The facility, which created X-23 is like a branch of weapon x. They come in and cause some of havok, also they play a small role in messiah complex via their creation. The character X-23 becomes a major character latter on and there are some references you wont understand unless you read her two mini series.