Of course the savage rascal is the best choice if the kids are little (6 and under). It is a brilliant kids rifle.
Another choice that has a much cooler "look" to it is the T/C hotshot. These guns have lots of fans too, a break action and an exposed hammer. They are very cute, and still are stocked in some stores for around $300.
I think a single shot cooey (etc) 410 shotgun is a great choice. I have seen kids as young as 6 love shooting these, especially if their older siblings are excelling with a .22 while they are struggling.
If the kids are bigger, you can look at other choices. I would consider getting a norinco jw-15 with the short barrel. This is a cz 452 knockoff with a synthetic stock. My Canadian Tire has it for around $200 right now. If you shorten the stock (with no regrets) and fashion a butt pad, this becomes an awesome CZ scout style rifle. It has open sights and can easily be scoped. Since they did a faithful copy of the cz, these are really nice as well, though the mags are not as good as the CZ ones, they are interchangeable.