As a Muslim man, according to Islam, can I marry a woman who is not Muslim?
Whether a Muslim man can marry a non-Muslim depends on a couple of things. First of all, if he is Shi'ite, the answer is no, at least not if we are talking about nikah. Mutah is another matter. A Shi'ite man who wants to permanently marry a Person of the Book can contract a mutah marriage for a period sufficiently long to exceed their lifetimes, for example 99 years.
If a man is Sunni, mutah is obviously not an option, but he can contract a nikah with a non-Muslim - if she is a Person of the Book who seriously practices her faith, so for example, she conducts her personal life in a pure manner.
What would be problematic, though, from an Islamic standpoint, is if she insisted on putting in the aqd that she reserves the right to educate the children in her own religion, so that it is not a foregone conclusion that they will be Muslims. And for a serious-minded Jew or Christian, that will definitely be an issue. It may well end up being a deal-breaker, especially for a Jew, as under Jewish law, the fact that your child's mother is Jewish will mean that the child is Jewish.
In the case of a Jew, it is also problematic for them to marry a non-Jew, because under Orthodox Jewish law, it is impossible to contract a religiously valid marriage between a Jew and a non-Jew. So that under Jewish law, you would be considered to be living in fornication. Your children would, however, be considered legitimate.
Many Christians also believe that they should not marry outside the faith, but it is not viewed as fornication if they do. The marriage will be religiously valid.
Also, be aware of two things with regard to a Christian in particular: 1) a serious-minded Christian will view divorce as essentially not permissible, and you will need to go into the marriage with the express assumption that you will be together for life; and 2) a serious-minded Christian will also view polygyny as adultery.
I realize that it is legally problematic for an aqd to divest the husband of his Islamic right to have up to four wives. But for the good of your marriage, you need to have a provision in there that you undertake to have only one wife as long as you both shall live, and that should you not keep this promise... basically, your marriage to the Christian woman shall be dissolved.
Exactly how to word it, you would have to consult your imam, but it would be something like this: should you contract a marriage with another woman, or should it come to light that you already have another wife, then your [Christian] wife shall be entitled to a divorce with immediate effect and without financial penalty.