BB guns are great to start....I had my first given to me as a first communion gift! I was a bird and chipmunk hunting fool as a kid and when those critters figured out it wasn't safe.....my action figures where next on the list! Spending time with a kid outdoors will create memories you will never forget. They just see the world differently.
I was at a family reunion once and my cousins little boy wanted to go for a walk in the woods, so I agreed to take him. He was roughly 5. We start walking and talking and the first thing he does is find a stick to beat the crap out of everything we walk past. When he found a bigger stick...he would "upgrade". I showed him acorns and deer tracks and we splashed in the water and mud a little bit. And then it happened. I asked him, "Noah, you know what kind of tree this is?" He stepped back, looked it up and down with a real serious look and said, "Big!". Well, obviously that wasn't what I was looking for, but it demonstrated how he looked at the world vs my perspective. We where gone for almost an hour but we had a blast in the process. He wanted to investigate everything....and I let him. I doubt he will even remember that....but I will. Make it fun, have fun and introduce details of information slowly. Becoming a hunter will take years. I started my boy fishing and small game hunting and then taking him with me deer hunting. Now he hunts on his own, reads deer sign, understand how to read terrain features, understand thermals and how we as hunters and even the deer use the wind.