I have never been married but would love to if it is God's will for my life. However at this late stage of my life, I could probably only marry a divorcee or widower. Is this OK?
In short, you are free to marry a man who has never been married before or a widower. We have a lengthy article concerning the Biblical view of marriage (and remarriage), which can answer this question in more detail. Meanwhile, while we hope the Lord leads you into marriage given your desire, you can also take encouragement in Paul's words from our 1Corinthians study:
1Cor. 7:32 But I want you to be free from concern. One who is unmarried is concerned about the things of the Lord, how he may please the Lord;
1Cor. 7:33 but one who is married is concerned about the things of the world, how he may please his wife,
1Cor. 7:34 and his interests are divided. The woman who is unmarried, and the virgin, is concerned about the things of the Lord, that she may be holy both in body and spirit; but one who is married is concerned about the things of the world, how she may please her husband.
1Cor. 7:35 This I say for your own benefit; not to put a restraint upon you, but to promote what is appropriate and to secure undistracted devotion to the Lord.
If God has gifted you with a life of singleness, then you are privileged to serve Him without distractions. Though you may desire companionship (and this is understandable), singleness is held in high esteem in scripture as a special position for serving your "husband," the Lord. Paul says this is not a restraint, meaning we are free to choose marriage if we wish, but he advocates for the benefits of singleness in ministry.
On the other hand, singleness must be gifted to you by the Lord, or else you are at risk of "burning with passion," Paul says, leading to the potential for lust and sin. Paul says it is better to marry than to risk sexual temptation and sin. Therefore, unless you have been gifted to live a single life, you should seek to marry one day.
As you pray for the Lord to send you a husband, we recommend you also pray for wisdom as to whether the Lord has selected you for singleness so that you might serve Him in unique and powerful ways unburdened by the need to care for a husband. Your faithfulness to such a call would bring great joy and eternal blessing, should you determine this is the Lord's will.