To migrate your website to a new server you need follow these steps:
(We consider that you have the latest version of the script)
Backup your database (from the Admin panel → Backups)
Backup all your website files (from the Admin panel → Backups)
Make sure you have all the components required on the new server, etc.
Unzip the backup file and upload the website files except the /public/storage symbolic link file on your new server.
NOTE: You have to make sure that all hidden files (the /.env and the .htaccess files) are uploaded to the new server.
Don’t make a fresh install
Create a database for your new server
Import the backup database (using phpMyAdmin)
Open the /.env file in a text editor and edit it as you needed (Edit APP_URL if your domain has changed. Edit DB_* vars if your database settings have changed).
You are done.