What would you recommend for a healthy non-toxic flooring that is not too expensive?

I recommend using any non-porous, hard surface that is labeled non-toxic and easy to clean. Suitable examples include engineered wood, certain natural stone, and porcelain tile. Be sure that all the materials used to install it are non-toxic as well, i.e., glues, adhesives, sealants, thinsets and any bonding agents.