When it comes to placing or answering a personal ad I don't think that there is an advantage or disadvantage to having or not having children. Some people, even those without children, prefer to date people who have children. Some people are neutral. Others would never consider dating someone with children.
If you have children, you should mention that fact and the relevant details as early as possible. If the fact that you do or do not have children matters to someone else, you might as well find out as soon as possible. If you are placing an ad, I think that you should state in the ad that you have children. There are many ways to say that you have kids. I see "active mom" or "custodial dad" frequently used.
I think that it is smart to tell the ages of the children and mention any special circumstances such as if the other parent has custody, whether a child has special needs, or that your children are grown up and gone. Things like that can make a difference one way or the other.
If you don't want to date someone who has children, don't say, "I hate kids." Use a bit of tact and say something like, "I prefer to date a man (or woman) without children." It will eliminate many people who have a lot of the other characteristics that you seek. But, if you really don't want to date someone who has children, especially if you really can't stand children, clearly state your preference. If you're one of those who are neutral on the issue, discuss your ambivalence if someone responds who sounds interesting and has children. You might find that you love children after all.