If you have the luxury of picking your stack, and don't mind using modern, clean PHP, try Laravel and Forge.
Laravel is a solid framework, and Forge handles the deploys, even going so far as to be able to deploy automatically when you push to master. Plus, you can use Laravel Spark to build an application framework base, with user login, teams, payment, all that written for you.
If you're not able to pick your stack, well, Ansible is pretty easy to learn. You can use Vagrant for the local dev, and ansible-vault for production secrets management. Deploys become a single command line, and that includes when you want to push an environment update.
Laravel + Laravel Homestead (Pre-configured Vagrant VM) + Laravel Forge [2] (Server config + deployment processes) makes my life too easy.
It doesn't even have to be a PHP/Laravel project for this process to really make your life easy.
The Homestead VM has the same services installed and configured the same was as the forge server. Nginx (or Apache), mysql/mariadb, postgres, sqlite, node/bower/grunt/gulp, redis, memcached, beanstalkd, elasticsearch, go, etc
Homestead has pre-built commands to make it very easy to add new sites/projects, does the port forwarding for you, handles the shared folders easily. Forge's UI allows you to not have to ssh into the server for things like restarting nginx/mysql/postgres, 2 click let's encrypt SSL certs, configure/restart queue workers (via supervisord), configure cron scripts and schedules, deploy via git with custom deploy scripts. You can create databases, create database users and manager their permissions. Create firewall rules and manage daemons.
I spend all day in the PHP/Laravel ecosystem so it works for me - but I find myself pushing non-PHP products through the same pipeline most of the time because it's so easy and just works.
Laravel is a solid framework, and Forge handles the deploys, even going so far as to be able to deploy automatically when you push to master. Plus, you can use Laravel Spark to build an application framework base, with user login, teams, payment, all that written for you.
If you're not able to pick your stack, well, Ansible is pretty easy to learn. You can use Vagrant for the local dev, and ansible-vault for production secrets management. Deploys become a single command line, and that includes when you want to push an environment update.