The greenest floor coverings are "hard" surfaces.
Carpet can present problems with off-gassing of volatile organic compounds (VOCs), and can hold dust and allergens, but is often used because it is fairly inexpensive.
Stained concrete is also fairly inexpensive, but some homeowners find that it is uncomfortable to stand on for long periods of time, and things dropped on it break easily. Also, depending on your climate, concrete often feels cold to the touch in winter months, plus it is acoustically "live."
Tile is a great choice for wet areas, like bathrooms or kitchens - if you use tile, try to limit grout joints to 1/4" width or less.
- You can get some attractive porcelain floor tile furnished and installed starting at around $5 a square foot and up, depending on your taste and local market conditions.
- It's not as fragile as you think, but if you are installing it over framing, be sure to use a backer board (Hardibacker or similar product) between the subfloor and the the tile to minimize the chances of cracking due to structural movement.
- When installed directly on a concrete slab, consider a liquid "anti-crack" membrane.
For common areas and bedrooms, there are some great alternatives to traditional hardwood flooring, like bamboo flooring, which is relatively affordable (starting around $7 per square foot installed), and is a sustainable choice, because it is rapidly renewable.
You could also look at laminate flooring, which has the look of wood, but contains composite material.
With any flooring that is secured to the substrate with an adhesive, remember to request a low-VOC adhesive formulation. Look for the GreenGuard label or similar programs to help identify these adhesives.