Let me start by saying that I have moved dozens of websites from one server to another, without issue.
I recently moved a website and when the URL is visited, a file named “download” with no extension and only a 1KB file size downloads automatically. I backed up all files and downloaded the databases using four different methods, just to make sure: BackWPup, BackUpWordPress and manually by zipping the files & downloading the files via FTP.
The original website works perfectly on the original server.
I used the method I’ve always used when moving to a new server.
On the new server:
Create new DB, user and import database
Upload files and unzip
Edit wp-config.php with new DB name, user, password
Mini Militia App Lock 7Zip