Christianity and Islam are very similar in their beliefs of Heaven and Hell. Both believe that if you lead a righteous life and are true to God that you can ascend into Heaven. Or if you are wicked you are punished to Hell. The biggest difference between Islam and Christian beliefs of Heaven and Hell is how someone may enter Heaven, and how they are rewarded. For Muslims the highest spot in Heaven is reserved for Muhammad, and that based on your good deeds you will be rewarded better or worse than others when you enter Heaven. This also means not only do you have to accept Allah into your life, you also have to be practice the teachings of Muhammad and exhibit them in your everyday life. The more you are able to reflect the prophet the higher level of Heaven you can achieve. This in contrast to Christian belief that it’s important we praise sinners who repent and accept them and praise them, just as a shepherd praises the return of his lost sheep.
The idea of a virgin birth caused by God would be appealing to a Greek audience as they were very accustomed to half-gods or even demi-gods, and it brought the idea of a Christian God into the physical world at the same time. The three shepherds who are visited by the angel would also give the Greek audience a more direct link to divine power they desire, making Christianity that much easier to accept.
I believe the fact that God accepts even those that have sinned into his heart very important to the people at the time. They were no longer looking for answers to everyday things that the Greek and Roman gods could give but rather a spiritual answer. The fact that Greek and Roman gods squabbled about human events made them seem very mortal in their own sense. Being able to accept an omnipresent God into their life would serve to strengthen the people’s relation to God because no longer are peopling about invoking God’s wrath, but rather seeking his guidance. Making it easier for people to trust in and God and practice his teachings.