Hi energizedchris,
In case you haven’t read it yet … the first place to start your research is post #1 here which has all the basic information, steps, and guidelines and links to some of the forum posts that you will find most helpful.
You are asking a very complex question that has no specific answer because it depends on how each person answers the question 'how safe is safe enough for me?" and this can be different for different people. Post #2 here has much more information about the “safety” of mattress materials and components but “most” people would consider Tempurpedic to be “safe” although there are also a minority who are more sensitive or that are more focused on natural materials that wouldn’t agree and have experienced symptoms of various kinds on Tempurpedic or other memory foam mattresses. I personally would tend to avoid memory foam for babies or young children (if they will be sleeping on the mattress) both because of potential offgassing issues in some cases and because memory foam is generally too soft and “motion restricting” for babies and young children.
I would follow the steps in the guidelines and choose a mattress that was the best match for your personal value equation. I’m happy to help with “how” to choose but the specifics of “what” to choose is up to each person and their unique criteria, budget, and circumstances. The post also includes a link to a list of some of the better online choices I’m aware of.
Phoenix