Well, of course, this is just personal opinion, and I don't know how big your little brother
is, and how responsible, etc. But, I just think 10yr old is a little young to be starting with
such as a 30-30, etc. I'd be inclined to get or give him a good single shot or bolt action
22LR rifle, and get him out small game hunting to start. Then, in a few more years, then
get/give him a big game rifle or shotgun.
Also, small game seasons are longer, and ammo is cheaper too which can make for a lot of time at the range having fun shooting targets, pop cans, etc.
Something to think about - just my .02