First and foremost it will be a great way to spend some quality time with your son or daughter. (Yes boys can work with yarn too!)
Cowls: Now, here is a project that is hotter than hot. Cowls, aka mobius knitting is all the rage right now. And no wonder. These little beauties are attached at their ends when finished and they are also called Infinity scarves. Besides looking just terrific with any wardrobe, cowls are the best warmer-uppers on cold winter days. Easy to knit, they can be finished in a weekend.
It can be a great asset for when the child becomes a teen as this is usually a time when there are many differences between the parent and the child. Any kind of needlework which you share can help to eliminate differences, tensions, and arguments, and bring you closer together.
Other smaller accessories that can be particularly useful when working on a knitting project are stitch markers, which can be used to mark particular points in a pattern that you are working on. These often come in the form of small rings which can simply be slipped onto your knitting needles as you knit.
Finally, one essential accessory to keep your equipment safe is a set of knitting needle caps, which are designed to be placed over the end of your needles when they are not in use. As mentioned above, needles can cause damage to bags that they are kept in, and can even prove a safety hazard, especially if they fall into the hands of children.