Onward ... to the weaponry!
Speaking of Rick's son, Rick Grimes also carries a handgun. He's a little smarter about it, being a sheriff's deputy and all, and carries his in a holster. Rick is also good at using any available weapon found close-at-hand. The knife, or any other handheld weapon is great for conserving ammo and keeping quiet but understand that one must get real close and personal to force the edge of a knife into the skull of even the most dastardly zombie. Most will find it hard to gather the required intestinal fortitude to get this close. Besides, it is actually quite difficult to put even a sharpened blade through a skull. It's one of the hardest and well-constructed bone structures in the human body.
It would also be a good idea to pick up the biggest knives you can find, along with whatever garden tools they may have. A pick axe handle could save your life.