I recommend true linoleum which is not the same as the vinyl floor that most people call linoleum. True linoleum is made from mostly natural products, has a strong smell of flaxseed initially because it is made from flaxseed, but we had no reaction to the smell at all and we're quite sensitive to smells.

It's beautiful, easy to clean, and, unfortunately, not cheap.

http://www.themarmoleumstore.com/fra...px?menu_id=123

I'll also caution you that you need to make sure the people you hire to install it know what they're doing if you go with sheet linoleum. They do make a version that is something like Pergo but topped with the marmoleum instead. We didn't want to raise our floor and I didn't like the smell of it in the store (of course the whole flooring store stank to high heaven, IMO, but that's another story).

FWIW, this is the color we chose:

http://www.themarmoleumstore.com/fra...hite&border=60

And it is absolutely beautiful.

Hardwood and cork are also beautiful options. I personally wouldn't go with even wool or cotton carpet for 2 reasons. 1 because they would still need padding and much of the off-gassing comes from the padding. 2 because carpet by it's very nature holds in allergens and dirt. Hard floors don't. If you want to use rugs on the hard floors that's great and you can get them cleaned much better than you can ever truly clean carpet.

Rachel