+1 on a Ruger 10/22 rifle. Get the basic model - they can be found all day long new in the low $200 price bracket. There are nearly limitless upgrades and gadgets to personalize it with down the road which is fun to do.
Bolt action is great but I think the semi-auto will be more entertaining in the long run. You can always start the boys off with just 1-2 rounds in the rotary magazine to enforce quality shots and limit Hollywood style shooting.
