Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

Marrying a Muslim woman is better as indicated in the following Hadith: Abu Hurairah (May Allah be pleased with him) reported: The Prophet (PBUh) said, "A woman is married for four things: for her wealth, for her lineage, for her beauty or for her piety. Select the pious, may you be blessed!". [Al-Bukhari and Muslim].

On the other hand, marrying a non-Muslim woman under the condition that she converts to Islam involves some risks:

1-What if she refused to convert?

2-Her converting in greed of marriage means that it wasn`t purely intended for the sake of Allah while Allah doesn`t accept but that which is done purely for His sake.

3-She must remain influenced by some non-Islamic manners and customs, and it can`t be guaranteed that she abandons them.

However, if she converted before marriage and became a devout Muslim, then she is treated like any other Muslim woman. And Allah the Almighty knows best.