C&C cages are made up of the grid that you have seen on amazon, and something called corex for the base. This is like thick plasic sheets (the same as would be used for an estate agent sign)
The grids are 14 inches high and piggies are not born climbers, I have never heard of one escaping a cage, and if you dont have other animals (for example cats and dogs) there is no need for a lid.
The C&C cages can be made as big as you like, in any shape to fit your space. Most people on this forum use fleece, as it is very cost effective, doesnt cause health problems in piggies, is nice and soft and cosey for them and looks pretty too. (if they are your childrens pets, its a great excuse to show them how to use the washing machine too! hehe)
I'm sure youve researched this already as you seem to be doing your homework (which is great!) but please be aware, when you first get your piggies they will be very scared, and need a little time to settle in. Dont handle them (as in keep getting them out of the cage for cuddles) for the first day atleast so they can get used to there new home.
To help the piggies get along, if you have the space its best to have two of everything, for example, two hideys, two food bowls, two water bottles, two hay places (maybe a ball and a rack or a rack and a toilet roll tube with hay in)
Piggies need 1 cup of fresh veg per day per piggy but this should be introduced slowly to young pigs (there is more info on this in the food section, ie what foods are ok to feed and how often to feed them)
Growing pigs also need unlimited pellets of musli, whichever you choose to feed.
All piggies need unlimited hay, as this should make up 80% of there diet.
Another benifit of getting a piggy from a rescue, is the people there will be able to tell you about the temprament of the piggy, and between you you can decided which pair will suit your family best (ie choose a gentle affectionate pair, maybe a little older than babies, that way your children will be able to handle them more and they wont be as skittish)