I suggest to you before all else that you pray to God to guard your heart and mind, because, truly, the 'wisdom' of this world has caused many to lose their eternal life. If you are Orthodox, partake of the Holy Eucharist in your Local church and devote a few days to prayer and contemplation on God's word. Then come with a fresh mind to assess where you stand.
For the wisdom of this world is foolishness in God's sight. As it is written: "He catches the wise in their craftiness"; 1 Corinthians 3:19
Both sides are capable of presenting defenses to satisfy their own faith. So really this isn't a battle of who can satisfy you with the better or more convincing argument.
As St Nikodemos said "the battle for heaven and earth is in the heart".
So retreat back to God, to His church, speak to your father of confession receiving his aid and advice, then make your own decision. At the end of the day it won't be our words that'll compel you to the truth. Because even if we were to convince you, it will have been merely on an intellectual level.
That is not to say that you discount all that has been said thus far, for it is important to have knowledge and proper information. Absorb what you can from what has been said and pray to God with an open and honest heart.
I'm reminded of a story of a Muslim man who traveled to the United States to proselytize and spread Islam as best he could. He got into a serious car accident while there, and a Christian man happened to take him out of the car and took him to a nearby hospital. While on his bed he asked the man why he helped him. The Christian was simple in his answers. He, like the Samaritan, felt love and compelled to help all those who Christ put in his path. He told him that Christianity demands love, even to non Christians.
The Muslim man was utterly confused, and began to pray. He'd been taught differently his entire life. He was taught to view non believers as misguided, with no real morals, or virtues. He began to weep deeply and cried out to God asking Him to reveal Himself, to show him His true self and who He really was. He heard a voice saying, I am Jesus Christ, the God of Abraham, Isaac and Jacob.
I heard this story second hand. I'm not denoting it's true or even unchanged, but the principle is there and it's a fact that many stories of this kind happen daily all over the world. 'you will know them by their fruits' Christ said.
Let me tell you, I'm Coptic Orthodox so in Egypt we've experienced and still experience what Islam is doing. It cannot be sustained. It is a way of life that would implode under its own weight. Time and again this has been shown in history with Muslim empires collapsing because different groups believed the other was wrong, etc. I know this isn't any kind of solid argument but it's the witness of history and what we have and witnessing today.
If you want real solid proof of their falsity then read especially these articleshttp://www.answering-islam.org/Quran/Text/index.html
It pertains to the textual integrity of the Qur'an. It makes the convincing argument that the Qur'an was plagiarized rather well from the Gospels and from Apocryphal Gospels too with the help of the excommunicated monk bohaira and others.
Again all those are arguments that can't truly bring you to true faith in Christ.
But they can at least make you see the error of Islam.
St Paul said 'For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.'
Even St Paul knew it sounded foolish just as Muslims and Atheists today see it as.
But St Paul through the Holy Spirit again said 'But God chose the foolish things of the world to shame the wise; God chose the weak things of the world to shame the strong.
You may have heard all of this before, so revert to my first paragraph because that's the most important thing before you undertake any other task.
God bless and we'll be praying for you.