is the way to go.
That way, each child gets their own everything, including their own iTunes.

Sharing the Apps may be another story though. You mentioned creating an iTunes Store account for each of them which means that items purchased from the store are only for the use of the owner of the account. Sharing is not on the cards here.

Home Sharing allows you to share the music and apps with another computer, not iPod, within your family.

Technically, swapping music between iPods is stealing as would be the swapping of apps. That said, if all the iPods were running off the same iTunes Store account, the apps would be allowed on each of the devices owned by the iTunes Store account owner.
That would also lead to disputes with the gift cards though.

More details on Home Sharing can be found here: http://support.apple.com/kb/ht3819

P