All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
First of all, you should know that marriage is a long journey traveled by both spouses together along with their children who need a good, righteous upbringing. Since the mother bears a bigger share of caring for the children, the Muslim man should carefully choose his future wife; he should be keen on choosing a pious, righteous woman. Abu Hurayrah narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said, “A woman is chosen as a wife for four things: her wealth, her lineage, her beauty, and her religiosity. So win the one who has religiosity, lest you be a loser.” [Al-Bukhari and Muslim] In another hadeeth on the authority of ʻAbdullaah ibn ʻAmr the Prophet, sallallaahu ʻalayhi wa sallam, said, “The world is but a temporary enjoyment; and the best enjoyment of the world is a virtuous woman.” [Ibn Maajah]
It is essential that you use rational judgment, rather than emotions, in choosing your future wife. Yes, you are allowed to marry this girl, even despite her neglect in observing the prayer and her ignorance of her religion. And yes, you bear no sin if you married her and she does not progress, as long as you have done your duty and offered her advice as due. However, you may regret your choice later on when it is too late, and you would be left confused on whether to divorce her or keep her with her bad state. Abu Moosa Al-Ashʻari reported that the Prophet, sallallaahu ʻalayhi wa sallam, said, “There are three individuals who, when they supplicate Allaah, their supplication is not answered: ... and a man who is married to a bad woman and he does not divorce her...” [Al-Haakim and Al-Bayhaqi]
Al-Munaawi commented on this hadeeth, saying, “The hadeeth refers to a man whose wife has a bad character. If he does not divorce her and supplicates Allaah against her, his supplication is not answered because he is the one bringing such an evil upon himself by retaining her while he can divorce her and spare himself the suffering.” [Faydh Al-Qadeer]
If you do not marry her and she relapses because of that, you bear no sin for that since you are not obliged to marry her in the first place. However, we advise you to seek the help of some pious Muslim women to give her advice and teach her the matters of her religion; perhaps Allaah will bless her with steadfastness on the right path.
It is permissible for the Muslim man to marry a woman from the People of the Book (Christian or Jew) provided that she is chaste. It should be noted, though, that some scholars held that it is disliked to marry a Christian or Jewish woman given the evil consequences that such a marriage may incur. The Kuwaiti Encyclopedia of Fiqh (Islamic Jurisprudence) reads:
“Although it is lawful for the Muslim man to marry a Christian or Jewish woman, some scholars held that it is disliked because it is feared that his infatuation with her might tempt him away from his religion or closer to hers. ʻUmar ibn Al-Khattaab said to the Companions who married Christian and Jewish women, ‘Divorce them!' Imaam Maalik was one of the scholars who held that it is disliked to marry a Christian or Jewish woman because she feeds on wine and pork and feeds his child with them through breastfeeding ... and he is not entitled to forbid her from wine and pork, even if he is harmed by their smell during their intimate time together. Also, he cannot forbid her from going to church, and she may die while pregnant with his child and would then be buried in a non-Muslim cemetery where her grave will be a pit from hell, and her child, who is part of his Muslim father, would be inside her womb in that pit...”
Allaah knows best.