Most of the stories I have read turn it into an all-out worldwide nuclear war. With the missiles I worked on (**** Hercules), we had two types of missiles: high explosive and nuclear. Each of them could be fitted with either an arm plug that would make the missile either surface-to-air (to take out other missiles or planes) or surface-to-surface (to take out land-based installations). I think your story might work well with our missiles taking out most of the incoming missiles (Sprint missiles were designed to do this very thing on a moment's notice), yet having some come through. There would definitely be EMP effects from the missiles destroying each other, and some fallout, but the most fallout would come from the missiles that got through.
It might be nice to have a crippled society, since most of the government would survive in shelters, but the preppers would bear the brunt of bringing stability to the country in the short run.