Lots of important questions and ideas in this thread.
To the OP, my feeling (take it for what it’s worth) is that you’re closing yourself off to some potentially great men. I understand wanting someone who is able to have a valid sacramental marriage. That’s a moral and faith issue. But to shut yourself off to the idea of anyone with an ex-wife or anyone with children is to rule out 99% of the population. If you define a good man down that narrowly, of course there are no good men.
For myself, I would love to marry a wonderful Catholic man someday, someone who is strong in his faith and shares my values. Yet, I currently go out to dinner and plays frequently with a male friend who practices some cobbled together semi-self-created form of what he says is closest to Shinto-ism. He has lived a very un-Catholic lifestyle, to say the least.
The question is: what is marriage about? According to our Catholic faith, the purpose of marriage is to help one another grow in faith and get to heaven.
I can say that my ‘Catholic’ husband and my ‘Catholic’ parents and sister have done little to help me grow in faith or to encourage me. They have more often torn down my trust in God, torn me down as a person, destroyed my sense of worth, and at the very worst, XH’s lies had me literally fearing I was going crazy, unable to trust my own senses, staring at things, hearing things, and wondering if they were even true. (Look up gaslighting–it’s what he was doing.)
This man, by contrast, has encouraged me repeatedly and consistently to live my faith. He reminds me I’ll find peace in the Adoration Chapel. I have at times gone more often as a direct result of knowing he’d remind me of that and encourage me to. He reminds me that faith is a challenge even to the great saints, and when I’m frustrated with the seeming continued attacks coming at me, reminds me faith is not about being handed an easy life. Yesterday when I was feeling like turning from my faith, one of his reactions was to check if I’d taken off the crucifix I always wear. Despite his own past and even his current feelings about sex, he has committed to doing nothing with me that would be against Catholic teaching or disturb my conscience. I have become a better, stronger person, better able to live my faith, as a result of being with him. His profound and many kindnesses have given me healing and helped me grow in forgiveness toward and compassion for my mother–thus he’s directly helped me grow in Christian virtues.
In turn, he has done a great deal of changing and growing; he has returned to daily prayer and is reading a Christian apologist, not because I asked him to, but simply because we went to see a play that got him interested in this particular author. He has changed his lifestyle dramatically–a decision he made on his own–as a result of being with me and being influenced by me in turn.
I do still feel that the ideal is sharing a faith, and yet my experience tells me that marrying a ‘good Catholic’ is no guarantee of having a good marriage that lifts both people up and brings them closer to God. Given a choice, I would take the person who brings me closer to God, and that won’t always be the Catholic. I wish all Catholics were that good and holy, but sadly, it just isn’t true.