Why did they choose Stevens to go into the Source Code?

Capt. Stevens was very much needed by the project as stated by Dr. Rutledge. There has been many trials on this project but nothing was successful. At last they had found Capt. Stevens who can be used for the successful run of the project. So it isn't like he was the first try, but he was the first successful try.

As no physical activity is needed for the program, Capt. Stevens was fit for it and finally he achieved the goal successfully.

As to why they used somebody ignorant of Source code, there can be two reasons.

1) It was not a public project. So anybody who would join the project would certainly be ignorant of it until he is in the project.

2) The knowledge of how Source code works is not really needed for the agent to work.

EDIT- Here is the part of conversation that is very useful in understanding my point.

Rutledge-Look, if we can get the funding, I guarantee we can have at least... Eight source code projects up and running by the end of the year.

Rutledge-Let him die? He just saved millions of lives today

Rutledge-For all we know, he may be the only candidate with which the system works. So, let's clear his memory and reinitialize source code.

I remember couple of lines said by Dr.

"A soldier can (wants to) serve even after he is dead."

"We found his age and body suits you perfectly" (so they are not just choosy about Steve but also choosy about Sean)