Best way to move blog?

Hello all!

I am getting ready to move my blog. I need to move it to a new hosting account and URL. I am wondering what would be the best way to do this.

Should I:

back up the WP MySQL database and then reinsert on the new account?

or

Should I export the data to an extended RSS file or WXR file? and then import it?

I want the new blog to have all of the same post, categories and comments as the old one. Also, I might have different versions of WP running on each account. Do I need to install a current version on the old blog before i try to move the data over?

Any help that anyone has, would be great!