To take photos I would suggest putting your camera into the "Kids and Pets" custom mode. This should give you a good basis to shoot kids that are often moving around quickly. If you want to get more technical you could put the camera into "Av" or Aperture priority mode and set the aperture to be the widest value possible such as f/2.8-4.1. This allows the most light possible into the lens, and will freeze your subject(kids).
Editing comes down to personal preference. If you are looking for free software to get started with organization and cataloging of photos, Picasa by Google is a great choice. If you are looking to do more advanced manipulation of the photos then Picasa will allow, Photoshop Elements is a great option.