I read your post yesterday and didn't have time to respond. My situation was a bit different, in that my husband was infertile for many years. He had an accident that severed his vas deferens when he was 16 years old- basically a vasectomy but a ragged trauma injury, not a neat cut like a surgical vasectomy. For 20 years he couldn't have children, and he never had a girlfriend for more than one year. He was always up front about his condition, and women would date him but not get serious because he couldn't have children. I don't know how hard he tried to find a woman who wasn't interested in children, and of course this was before internet dating was big.
When I met him, he had been told by a doctor that IVF technology would allow him to have kids. We met online, and his profile said he wanted kids. On our third date, he told me about his situation, and that having kids with him would be a long and expensive process. I decided that I could handle that and we ended up married and now have IVF twins. Sometimes I wonder if I would have chosen to stay with him if I had met him before medical technology caught up with him. He is a wonderful, loving, smart, funny, fabulous guy and a great husband, but would I have been able to give up the thought of biological kids? I really don't know.
But I also know several couples who are in great long-term marriages and neither wants kids. And I know couples with happy families of adopted kids, or step-kids. For you, I would recommend being completely honest from the beginning. If you are open to adoption or step-kids, say you want kids on your internet dating profile. But tell anyone that you have any sense of long-term possibility with about your situation within a few dates- certainly before you have sex or get exclusive. You do not want to waste months or more of your life, and lots of emotional anguish, on a man who can't or won't deal with your situation.
I was married and divorced before this marriage, and I know how hard it is, even without the infertility situation. I'm wishing you all the best for a happy future.