Digital Ocean for Laravel 5.2

Up to now I have only used fully managed web hosting services like godaddy etc.

I would like to transition to digital ocean for improved performance and control.

Using digital ocean for hosting. I'm looking for the best current method of deploying laravel 5.2 web apps, maintaining the app using GIT and maintaining/updating/patching the digital ocean cloud server.

I think from what I've read the best option is to use the laravel forge service which would build the server environment including services like MYSQL and the new letsencrypt secure certificates.

So my requirements are-

Push app deployment linked to GIT.
MYSQL
PHP 7
laravel homestead
Mail server like mailgun
letsencrypt 
Nginx and LEMP on UNIX distribution appropriate for laravel
Composer

Is laravel forge capable of automatically updating required security patches, upgrades for PHP and MySQL etc?

Or do you need to maintain the environment after the deployment?

via Chebli Mohamed