When we argue with the people of the book (Christians and Jews) and even with anyone about religion we should use this simple plan:
1- We argue in the best way. Our geopolitical anger should not have anything to do with discussing religions.
2- We could be born Muslims or non-Muslims. Changing belief is not easy. We should let them know that very well. Use the word God not Allah since it has the impression of a different God and not the same of Abraham.
3- That is why we should leave some doubt that we may be wrong as Muslims. We even try to let them help us what Muhammad could be. They will say something agree but tell them however the argument against that is that. Make it more about logistics and finding the truth than proving that you are right.
4- I would use the word Quran is the most accurate for scientific reasons. As Muslims we do not say the Bible is corrupt or has corruption but we can say scientifically and historically Quran is the most accurate.
5- We have to accept every bad thing they will say about Islam and the contradictions in Quran as potential facts until we can disprove that to them.
6- We try to get them the best answer and if we do not know refer them to the right people.
7- The most accurate interpretation of the Quran would be from God. By definition our even best interpretation should be understood to them and us to be less than 100% accurate in some verses.
5- We should resist the temptation of criticizing them or putting them down. We should carefully pick the sentences that make our point and meanwhile make them keep their dignity and pride.
6- We should know the difference between what God says in the Quran to the people of the book and what we should say to them. God does not do politics. It is our job as Muslims to do the politics.
7- Our desire to convert people to Islam does not stem from our desire for domination but for the love of Islam and their own good.
8- Guidance is from God. You would never convert anyone to Islam unless God wants to.
9- If they would not accept Islam and are not convinced we are to keep our obligations to them as our brothers in humanity provided they do the same.
10- Religiously and geopolitically we are not in war against anyone unless he proved with his actions that he is on war with us. Even for our worst enemies they can change to be our friends any time.