Hi,
No unless you use Apache or theme from 10 years ago, there are no big issues involved. The fastest way do to this is manual:
-
check/change wp-config.php file with new host database and so on
erase old and reupload database (ie through phpmyadmin or so - don't forget to change urls in wp_options table if it changed - 2 or 3 urls that define your site base URL)
reupload all files in "brute" rewrite style - eventually check file permissions
Nowadays, there are plugins that do backups quite well too, for the next time,