Great topic. I think that Nabeel’s talks are great concerning what you are attempting to do.
Another thing that comes to mind is to treat both documents, the Bible and the Qur’an, as ancient historical documents. This way when you speak of them you can demonstrate a few things. First, the reliability of the Hebrew and Greek Scriptures, in terms of its transmission and sheer volume of extant manuscripts in our possession in comparison to the Qur’an, or for that matter any other ancient document is unparralled. Second, in quoting the Bible you will be using it as a historical document and there by remove the charge of quoting it as a Holy Book, even though it is the word of God. Third, since the Qur’an did not come into the picture 600 years after the NT was already written we can demonstrate historically that the Qur’an presents a Jesus contrary to the NT and other historical extra biblical writings. In terms of point three it is important to note that in presenting a piece of evidence it is always more reliable to have earlier attestation to the events in question and the recording thereof than later writings.
Some books to consider are:
History, Law, and Christianity by John Warwick Montgomery.
This is an excellent treatment of Christianity using the tools of history and the laws of evidence in presenting a case.
Another book is The Case for the Resurrection by Gary Habermas and Michael Licona.
Lastly, there is an article that speaks more of what I spoke about in the paragraph above.
It was worked on by Dr. Josh McDowell and Dr. Clay Jones. It is called the The Bibliographical Test. It was updated from an earlier work of Dr. Jones.
Hope this helps brother.