These are constructed on a special foundation with high density foam and individually wrapped coils. Now lets consider the fabric covering or ticking. You might want to consider a hypoallergenic ticking if you are allergy prone. Mattresses and box springs are often sold separately, but it is generally a good idea that if you replace one you replace the other. Buying in a set usually offers a cost savings, as well.
Box springs are fairly standard considering all the mattress options.
Remember to do your homework and ask lots of questions. It's an important discussion for you and your family.