Other than files, you need to also move your database. If you are use to the GUI, you know that there is limitation exporting and importing. This is especially true when you have a large database. Through phpmyadmin, it is also a lot slower compare to method whereby you export large MySQL via SSH.
mysqldump -u [username] -p [DB name] | gzip > [dbname].sql.gz
It will prompt for password, type in the password for this access to the database. You will get a file name exactly like what you have typed at the end of above command ([dbname].sql.gz).
Use an ftp program to download the file.
Because the file is compress, you are downloading it even faster, and you can un-compress it on your new webhosting.
To Import the large MySQL
mysql -u [username] -p [DB name] < [dbname].sql
** If you uses a different username and DB name in your new webhost, use the new value in the bracket
I hope this this will actually make moving your wordpress or your website to another webhosting much easier.