New to WordPress – How do you transfer existing WP blog to new hosting company?

I just began using WordPress via my new hosting company – Marathon Press. As a photographer, I have found several of the plugins available to be vital tools to use with my blog BUT Marathon wont allow me to plug them in or have access to edit the blog because it is in a subdomain. They claim it’s because of security.

I want to switch hosting companies to one of the ones listed in WordPress that offer autoinstall and other WP features. I am concerned about transfering the blog and still having it maintain it’s current look (blog.digitalbyderran.com) Please help!