Moving Wordpress to a different site (or system) can be tricky unless you know the internals of Wordpress.
There's a Wordpress plugin called UpdraftPlus that will backup a Wordpress site in it's entirety and store it on the server and, optionally, also send it to a third-party site for safe keeping (eg, Dropbox). You can then easily restore the whole site should it be lost. The backup/restore plugin is free but the authors also offer a 'migration' module for a few dollars; can't remember exactly how much but in the region of US$15 I think.
So for what it's worth I would just pay the fee for the migration module and just let it do its stuff. Simply restore a backup onto the new site.