Why was Misaka Mikoto chosen as the candidate for the Sister's project when she was just a normal child when they asked for her DNA map?
If I recall correctly, an explanation for this is hinted at by Mugino later on in S, although it is addressed in more detail later on in the novels. In short, Misaka was selected because of something called the Parameter List.


   It turns out some people actually are more predisposed to be espers than others. Academy City maintains a database known as the Parameter List, which seems to contain predictions/projections about how much potential an esper has. (The database is kept top-secret to prevent social unrest). Using the information in this database, the city prioritized development and resources towards the children with a higher potential, because these children would yield a higher return on investment.

 So the researchers took Misaka's DNA map even though she was only a Level 1 at the time because she was projected to attain a high level based on the Parameter List.