Inquires similar to yours have been posted here before on the site, so to make it easy for you (and to make it easier for me to type 
) I thought I’d just copy here for you some of the responses germane to your question:
[i]“Toxic” is a term for poisonous substances produced within living cells or organisms, although the term is often used in the mattress industry (and often part of some “fear-mongering” campaigns), but I think I understand your point. Most people that are looking for “non-toxic” (toxicity is dose-dependent) materials are usually concerned most with “safety”.
As there is quite a bit of confusing information available online about toxicity, safety and organic, there is more about the different types of organic and safety certifications such as Oeko-tex, Eco-Institut, Greenguard Gold, C2C, and CertiPUR-US in post #2 here, and more about some of the differences between organic and safety certifications in post #2 here and there are also some comments in post #42 here that can help you decide whether an organic certification is important to you for environmental, social, or personal reasons, or whether a “safety” certification is enough, and what those certifications can mean to determine whether the contents of any particular mattress are “safe enough” for you.
The only reliable way to assess the “safety” of different materials in more general terms is based on lab tests and the certifications they have for harmful substances and VOCs (regardless of whether they are organic or natural or synthetic) so that you have some assurance than the VOCs are below the testing limits for the certification. If the materials in a mattress or the mattress itself has a reliable “safety” certification then for most people they would certainly be “safe enough” … regardless of the type of material or the name of the manufacturer on the label.
You may have read this already but just in case you haven’t … there is more information in post #2 here and the topics it links to about mattresses and children and “suitable” and “safe” materials including a link to some general guidelines for children in post #2 here. It also includes a number of links to the better forum posts and topics about mattress and children as well which have more information about many good options children which would be well worth considering.[/i]
Generally, for growing children you want something more in the “medium” to “medium-firm” range, due to their epiphyseal plate and postural formation. If you’re looking for something using polyurethane foam, I’d want at least CertiPUR-US certification for the foam. You’ll tend to find your best price with traditional innerspring style mattresses for this particular application. If you desire something more “natural”, but want to keep the cost as low as possible, you could do something like this or this. There are of course other options out there, but I’m familiar with these two as I’ve seen them before here on the site.
I hope that information is helpful!
Jeff Scheuer, The Beducator
Beducation / Mattress To Go