Shared hosting is probably better, and AFAIK more common, for the mildly dynamic website. The host handles a lot of the admin tasks like OS updates that you have to handle yourself with a VPS.
The environment is fully hackable and has PHP, SSH, SFTP, MariaDB, dominant languages like Perl and Python, obscure languages like Haskell and Lisp, etc etc.
Although I wonder how often your family actually uses it.