Here is something I have had success with when moving to a new hosting provider a very large site 29,000 posts and more.
ftp down all files from old site then using a tool like phpMyadmin export out your database, (if it real large you may have to split it up, I found I had to split mine into 3 parts to get it to import properly)
Then on new site upload all files downloaded, then create new database and import everything from the old one, then go and change the wp-config file to point to new database, user & password.
Good Luck
