The barrels were built for those leads BB's back then, don't try using any of the lead BB's in this one, it will jam. They are pretty much intro toys, good to wet an appetite and to move up from. There really is not much of a point to rebuild it with say a 499 barrel or a stronger spring, for the cost you can buy up. Why not look at something like a Crosman 760 or 2100 pump? What with the plastic stocks, they are light. With their pump ability, you can shoot low power with 2 or 3 pumps which any child will be able to do, or if the need arises, or as they grow, you can increase the pumps. They are rated @ 10 pumps and mid 750's with a pellet (slightly higher with a BB, another good point, they use both) but mine, at nearly 18 years old, has shot 850 with 13 pumps with a CP pointed. They costs can vary, but they are typically under $30. I still have one that is coming up on it's second decade. It is the one on the right-edit 3, my OTHER right,ie LEFT-geeze, brain drain this a.m.. Added a wood stock a couple years back. Still use it for close in (near the house, where power limits are preferred) varmint removal.
Oh, yeah, the reason for the edit, I forgot, they are accurate with pellets and BB's, more so with pellets
And Edit #2, you don't have to go Crosman, Daisy sells their line of equivalent items, although in my opinion, I think they are cheaper made.