This is kind of vast for the most part and I’ll do my best to answer it. So, I think for the most part the Americans biggest concern was Russia or Russian allies using Nuclear Weapons against them and then full blown out Nuclear War. Correct me if I’m wrong, but I also believe that it was also how fast the Russians were coming under possession of Nuclear Weapons and wanted to keep up with Russia in terms of their achievements as the Russians sent Sputnik 1 into orbit in 1957 and were the first to ever do something like so. (It’s why we have science class. Thank the Russians for that one) The Russians were pretty advanced and the US wanted to keep up. This could be seen simply as a peeing race or as a way to keep themselves protected and from going to war as both sides knew and understand what would happen should they use Nuclear Arms in war.
If you have any more questions or would like me to add more, let me know! :))