Moving WordPress to a new Host

Having not done a blog before I was guided to wordpress and love it. I didn’t know how well I would enjoy doing the blog and therefore didn’t want to commit to any particular host and especially didn’t want to put all the files on a host that I’m using for a forum I have. so I was guided towards using a free host. I can’t knock the host, they are great and all but I want to move my blog to my other host now that I know I def. want to continue blogging. Here is the catch, the free host limits how you can do things. and I can’t simply download my files and upload them to my new host without using an FTP. I find it so easy to just do it without the FTP, I know I’m crazy and will probably just do it that way. But before going through the hassle is there a way I can just download wordpress to my other host and simply restore it? I doubt it and I know I can move my blog via FTP. but if I can do it this way, I would prefer it. Thanks in advance.