FTP is an anacronym for File Transfer Protocol. The only purpose of FTP is to transfer your files from your computer to a remote computer (your web server). Though there are file permissions within FTP, this typically only comes into play when you are uploading/editing scripts.

Stats software and FTP are unrelated. If you want to do security or deny certain computers, IPs, etc from your site your internet hosting company can assist you.

As far as good stats software, I recommend Urchin or Deep Metrix. Both are relatively easy to use and provide the data most webmasters need. Additionally, there are many third party providers that offer hosted stats solutions. One that comes to mind is WebsideStory aka Hitbox.