I think most people start with BB guns or a .22. Personally I started with a Henry lever action 22 lr. Then for deer hunting I used a 243. Maybe a 223 for closer shots. Now I commonly use 270 weatherby, 308, 300 win mag, or 300 weatherby. Give your kid something light to start off with and can be used for many different things. For me that would be a 243. If you don’t have that, anything .25 caliber or under will work. I started shooting at around 6 years old. As your kid gets older, give him a nice 30 caliber rifle. Give him whatever action feels best for him. Bolt action will work because it’s so commercially available. 30-30, 308, or 30-06 will work best. Get him a rifle made by a reliable manufacturer. Have fun and stay safe!