Not knowing your location, grandson's size, age Etc. I would think a lightweight single shot bolt action rifle with iron sights would be the answer. A 20 gauge shotgun also might prove good considering location Etc. of your home and existing laws.The single shot rifle would encourage him to shoot carefully and learn accuracy as a semi automatic in the hands of a beginner tends to lessen the desire for accuracy figuring I have ten or more shots to hit the target. If it happens to be a squirrel or sitting rabbit one well placed shot is all that's required or at times time to shoot.I say this as a former certified NRA rifle, pistol, hunter safety and home firearms instructor. If the NRA is involved in or near your community their training and advice is fantastic. GOOD LUCK!

As a preface, my family has owned and operated a gun and ammunition shop since I was a child, I'm a NM game warden and a hunter education instructor since 1994, I train kids at the NRA Witington center here in NM every year and I answer this question often.

Most of us likely grew up with a handed-down lever action 30-30 as a first rifle- which in reality is the worst (and most unsafe) gun to start a child off with. It requires small hands to carefully lower the hammer on a loaded chamber every time it's loaded or unloaded. I caution parents against carrying on this tradition.

I agree with greenfinger, wholeheartedly. What is critical is that the gun fits the child- not almost or kinda fits. My 5 year old son has a tiny .22 rifle called a chipmunk, designed for small children, and in truth he is still too small to hold the rifle properly against his shoulder and still align his eye with the sights. We shoot it every now and then, but I won't be attempting to have any meaningful training sessions with him until he grows into it. If your grandson is still a little guy, I'd say a .22 chipmunk or another version called the cricket would be a good place to start (there are other manufacturers that build youth rifles, I'm not trying to advertise this one).

If he's a little older, I again agree with greenfinger that a single shot with iron sights is the way to go (and one that fits him). A bolt action would definately be a good choice, but I have a better suggestion. My older son has a hinge action designed for a smaller shooter. It has two barrels that can be switched out- one is a .243 rifle barrel (appropriate for deer hunting), and the other is a 20 gauge shotgun barrel (for ducks squirrels rabbits). When I was a kid I had one that had a 30-30- barrel, and a 20 guage, you can also get a 410 shotgun barrel. It's extremely inexpensive (concidering it's two guns in one), is safe, and would suite his needs into his late teens when he might grow into more specialized hunting guns. I believe the manufacturer is called New England Firearms.

hope that helps.

When I was a kid my dad bought a Marlin .22 rimfire lever action rifle. Probably was a better choice than semi-automatic rimfire as I am a leftie. Today the Ruger 10/22 .22 LR is a popular .22 semi-auto rifle. You should be able to find rubber extension pad for the stock if necessary.