We moved into an "older" home(18 yrs) in Aug and the carpets had never been replaced and were the most dirtiest I've ever seen! In my ideal world I would have hardwood/cork/tile everywhere

n my reality we had a budget!
The bedrooms were replaced w/ hardwoods(2 rooms we did/1 we contracted out), that left carpet in the room above the garage "playroom", hall, stairs and family room. After a lot of research and compromise I agreed to carpet replacement in those areas. Look at greenseal dot com and you can find list of carpets that are green seal approved and greenseal plus approved, the lowest voc. We went w/ finding a greenseal plus commercial grade carpet.
It was a lot of work on my part and most flooring stores will think you are speaking latin, after shopping around I found a shop that would look up w/ the suppliers to verify its greenseal status it was a blessing. I'm pleased w/ our carpet, there was faint odor the day it was installed and that's it! Like I said in an ideal world I would not have carpet and even w/ the greenseal plus is no garentee, but it is simply a compromise.....
good luck! btw, our allergies improved after the old carpet was gone....