Well, first of all, I'd like to say that I am glad you came here to ask before jumping into anything. Too many people rush things these days.
Go slow. Research, research, research. It is impossible to understate how important that is.
You need to figure out which bird is going to fit best into your home, especially since you have children. If this is your first bird, I do not suggest starting with a conure. You will be better off starting with a budgie or a tiel and then moving up to the bigger birds (personality-wise, not size-wise).
That said, conures can make good first birds if you do enough research on behavior, but because you have children, it would probably be better for you to gain experience with a different bird known for being a "beginnner bird." Conures may be small, but they take more knowledge and work than a tiel or a budgie. Because your kids come first in your life (as they should), it is likely you will not have as much time for training and may be more likely to let behavior reinforcement fall by the wayside.
If you have never heard a sun conure screech or a cockatiel scream, I would suggest you do so. Some people cannot handle these sounds. Whenever I go to a zoo or something of the sort and I hear birds screaming, it is always easiest for me to pick out the suns!
Cockatiels also create a powder on their feathers that can coat everything in the room in white dust if you are not very diligent about cleaning. This can also be a problem if you or any of your children have allergies.
How old are your children? How involved will they be with taking care of this bird?
Cockatiels, suns, and budgies can all make incredible pets if you know what you are getting into and are prepared for it. Remember, there are a ton of great books out there and Google is your friend.
(Try looking at a couple of the Barron's handbooks and books like Sally Blanchard's Guide to Companion Parrot Behavior. These can all be found on Amazon.com)
The best things in life are those who share it with you.
~Ashley