Dreamhost.
Very secure, very responsive and yes, you can use FTP. I assume you are interested only in hosting services, which is what Dreamhost does. Basically, you put your site up there and manage it yourself (although they have instant downloads of most content management systems such as Word Press, Joomla, etc. )
I built my own site because I wanted to do it as a learning experience. As an aside, I dropped Flash last winter because of frustration over not being able to have slide shows work on iPads. I am now powering the slide shows with a third-party option: Galleria. Although there are several other HTML-based slide show options out there.
You can follow the link in my signature to see the site in action.
