I have never been divorced, but my husband passed away 17 months ago and I have been dating different people for 14 months. In this time I have learned a lot about relationships, about my kid's feelings and about myself. You don't mention your children's ages, but no matter what, they will react to you having someone new in your life. Of course your situation is different. When I started dating I thought I was ready for a new relationship. It turns out I wasn't, and I was fortunate enough to find a man who loved me and loved himself enough to let me go, but helped me before he did. He explained to me that before you can have a healthy relationship, you have to be emotionally healthy yourself. This includes your relationship with your children. If you have an open communication line with them, you can explain to them, according to their age, that any healthy person wants to love and be loved. One thing I assure my child (the one old enough to understand, thus, worry) is that I would not be with someone who didn't love him. If the guy I got to love didn't love my son, then I wouldn't love the guy anymore. I am (and you are) a package deal. The person you choose and chooses you will have to accept that. And no matter how well they get along, there will be adjustments that EVERYONE will go through. Of course, one thing I ask for in a relationship is respect. You may not like someone, but you will respect that person nonetheless. It's not only your children that will react to him, he will react to them and you will react to both parties together. Another thing my friend taught me is that you have to be happy with yourself before you can make someone else happy. Regardless of the circumstances of your divorce, it is a loss that you grieve for a while. You may get a very supportive person, but you will try to make a life with him, and for that, you need to be in good shape emotionally. Do not expect your problems or your needs to disolve with a new partner. Sure you need a shoulder to cry, but he also has a life of his own and may need a shoulder to cry too, and you need to be emotionally stable to help him too.
Best of luck, and remember, there are many guys in the world, but your children will be your children all your life.