Lots of articles on this site, including gear lists--left hand column:
A bit heavy by BPL standards, but definitely lightweight. There's an excellent article there about backpacking with kids, too!
Another vote here for starting in the back yard, or car camping. It's especially important to become thoroughly familiar with your gear before going out. You don't want to be spending your first night trying to set up your shelter in the dark in a howling rainstorm with instructions in one hand and flashlight in the other! Once you've learned how to set up and take down your gear, cook meals, etc., try doing this in inclement weather. Skills in staying dry and warm no matter what the conditions are best learned where you can easily bail out if things get out of hand! Once you're confident in the car-caming scenario, then try going in a mile or two from the trailhead a few times and gradually going farther.