Praise be to Allaah.
The most important factors for a woman in choosing a husband are his attitude/behaviour and his commitment to religion. Wealth and lineage are secondary matters. The most important thing is that the potential husband should be religious and have a good attitude, because if a man has religious commitment and a good attitude, a woman has nothing to lose: if he keeps her (remains married to her), he will keep her on a reasonable basis, and if he divorces her, he will set her free on a reasonable basis. Moreover, a man who is religious and has a good attitude will be a blessing to her and her children, for they will learn good manners and religion from him. But if the prospective husband is not like that (is not religious), she should keep away from him, especially those who take the matter of prayer lightly or who are known to drink alcohol. We seek refuge with Allaah.
As for those who do not pray at all, they are kuffaar and it is not permissible for them to marry believing women. It is important for the woman to focus on the matter of attitude and religious commitment. With regard to the matter of lineage, this is a bonus. The Prophet (peace and blessings of Allaah be upon him) said: “If there comes to you (to propose marriage to your daughter etc.) a man with whose religious commitment and attitude you are pleased, then marry (your daughter) to him.”
But if you can manage to ensure compatibility (in terms of lineage and socio-economic status, etc.) as well, then this is better.